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Copy pathAp_ProgresionGeometrica.wxm
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Ap_ProgresionGeometrica.wxm
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/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 22.04.0 ] */
/* [wxMaxima: title start ]
Una inducción con ayuda de Maxima
[wxMaxima: title end ] */
/* [wxMaxima: caption start ]
FÓRMULA PARA LA SUMA DE UNA PROGRESIÓN GEOMÉTRICA
[wxMaxima: caption end ] */
/* [wxMaxima: image start ]
png
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i9qxY8foCB8/fhwwYAD5u0+fPioqKkwFZezYsQihjx8/kn/r6+vNzc3r6uooiiKbvljfeFNTUx6PN2zYMD6fTwdOmDABIVRQUMCMSVGUi4uLrKwsWVkl3Lx5EyE0ZcoUicpYUFDQrl27Tp06lZeX04HTp09HCJ04cYIZs7KyslevXgoKCklJSczwrl27vnnzhuPryL2gLi4urPCIiAglJaVRo0axDEUNDQ07OztmyOXLl+Xl5Wtra8m/mZmZMjIyAwcO5JgB/I/mN3HiROFHjZZRuBEfPXpE4qSnp/fq1WvTpk0RERHjx4/HGIeFhSGEeDze48eP6aQyMzNJ4M6dO+lAiqK0tbWtrKzoEIFAYGlpSfT75cuXI4RCQkLoumKmLyMjQ3R9AllzW7x4Mato3Gv406dPsrKyZKqFYG5uLi8vLzyP0BBfU6jmzJnz/PlzjPGTJ08QQrt376YfhYeHI4TI3gHCuHHjIiMjMcZjxoxBCA0fPpxZG1OmTEEI5eTksF5B7lZl6vT5+fkIIR0dHY4TQKwmMzY2pi1JjLGXlxdCKDo6WmQmaTOboqgxY8a4u7tXVFSUlpZ27drV0NCQNTK4ubnJycnl5+eTf3Nzc9u2bWtlZcVsu/nz59MNwcqYiopKXl4eifbw4UMbGxsya7Z06VKE0Pnz55nvWrRoEVOGMcZdunTZtm0b/S9ZDn316hXG+OPHj05OTiTc0tJSVVWVOcphbvLZNMkXT6NVREhMTNTQ0OjWrRvTls7Ozm7Tpg09FjWhCE0bHAjc+w7pejExMcxALmJGdy7ycdm3bx8zBYqipk2bxuPxmK3g5OSEEDp48CD519fXl8fjsQZbsguJtmMBAAAA4L9As4xSQmFh4Y0bN6ZPn06O1amqqn758oU82rFjx19//YUxTktLQwgx1+v4fH7btm2NjIzokBcvXixatAhjHBcXhxAyNzdnqmV1dXWysrJycnIsnbhTp07E3xIz0MfHR1j9Io4uJJ1+XrlyJULo6tWrzEB3d3fhVaCtW7cihJYtW0aHUBR15swZKysrWi1rFLILlKXL1tbWmpmZMe0uGl1dXTk5OWb6y5YtQwglJiaSf6urq/fu3SuRfvPnn3+yJhdoGi0jqxH79esnbJZs2rTp77//xhgfP34cIbRgwQLmU7JprUePHkzNlciPm5sbHeLv7+/p6YkxFggEnTt3VlNToyuBlf6KFSuY6V+8eBEhdODAAWagRDVMFmaZax3e3t7CewTE8NWEqqKiwtLSktTk7NmzEUL0uhzG+MCBA0xTqry83MbGhqIoiqLIcb7MzExmaiYmJurq6iyLIisrS1lZ2cLCgtlbY2JihFfSxEA32bFjxxBCR44cYT4lJhBZSmJlUk1NjWV2EubMmSNsJGCMp06dStuBGGNyoIBepCIwG4IlSxs3bhR+F9lvT9czISwsTE9Pj17iwxh/+fKFLP3RPcLf3//kyZPkV/RQmZqayhoqMWf5bILkN0qjVYQxpihq0KBBCKEbN27QcWpqaubOnUtGgyYXoWmDA4Fj36EoysDAoF27dsw0uYgZs3PNmjWL1bkwxufPn0cIjRs3jhl44sSJn376icymCQQCOzs7GRmZrKwsOoJAIGjXrl0TdvQAAAAAwDeNFIxSmoSEBLJn7/r16yTk06dPZPfs7t27EULe3t505NDQUITQnDlz6JCioiKygkEU0127djETDwoKEv7AEz1v2LBhzMC6ujqi/dCqJ2HixInc9xMSUlJS5OXllZSUmLuOBQKBlpYWS2morq4mC4NPnjzJzc0NDQ09e/Zsnz59xo8fz9LsxUP077dv3zIDiZVoaWnJUlNKSkrI6nRubi4duGvXLoSQsrLy5MmTz58/z8w5R6ZNm4YQio2NZYVzKSOrEclpMRa0VEyaNEm4sHv27EEI/f7778xAYgcyN0MWFRWRuQ+ip9K6r3D6rAUQclyWuXaBJaxhsuFQRkbG2dn54MGDTIWSC19TqOrr6z98+ECSUldX79y5MzN9civjp0+f6Mhkl2NsbKzwUnlhYSFCyNnZmfUKYv5t2bKFGSjpBBCryegpFQK5G+ny5cvCmZwxY4ZwavHx8TweT1ZWNjs7m/XI1tYWIXTt2jWMcUxMjIyMjHBDaGtr0w3Byhi9FZYJuWVk8+bNX758iYuLu3HjxtSpU21sbN69e8eMVldXR7wiWVpabty4kbmJg/kicpSXGGY0HOWzCZIvHi5VhDEOCAggy8jZ2dmZmZmvX7/ev3+/qanp2rVr6YXTphWhaYMDlqTvkMOokyZNYgZyETO6c5WVlSkrK3ft2pVZtLq6uk6dOiGEbt++3VD1EquVtY1F0gkdAAAAAPg+kNgopSiKpSgwIRoq63AOxtjGxkZBQYE+TIUx3rdvH0LowoULwomItB6JWXvp0iVm4P/+9z8ktMuXbFPU0tJinvEj0896enoSTT+vX79e2BKOjIxECE2bNo0Z+PDhQ4RQ27Ztvby8fvnllz179ty7d4/eJcgdExMT5oY3Qv/+/RFC+/fvZ0UODAxECMnLyzPn+D9//mxsbIz+oX379iz1VzwURenp6Yk8pitRGUkjilTiCcQNpp6eHmvlzdXVFSGUkZHBDFy1ahVinBplInKNgpk+qyD29vaysrJlZWXMQIlquL6+nphzBHl5eea56Eb5+kKF/9k7sH79emYp1NXVjY2NhSMTk/LUqVPMwAcPHqD/eyQVY1xWVka8nrJkjGyqZ9mWjSJyjYjP55MjdixrimRS5KzHxo0bEUKjR49mhfP5fGIWkhFs7dq1CCGyWZSGuARjNQSRJQMDA+FOUVJSQlzyLlq0aO3atbt27bp8+XJaWprIcea3335DDBYuXMgSfnJesW3btqwDpRLJp0SSLx6OVURc11pZWXl5eW3evPnQoUN+fn7k5G0zi9DkwYF73zl16hRC6Pjx4yJrQIyY0Zw7dw4htGfPHmbg8+fPEUIaGhq0UwNhyGwLy8Y+cuSIcO8DAAAAgO8eiY3S0NBQ+uyTML/88ovw3DDx3TpmzBhm4MiRIxFC6enprBQash6JOsJalZo5cyYS2g+2bt06hNCECROYgUSR8vDw4FDE/5/evXsjoc2ExD8Tc/cmHTh48GCJ0meRkZGBhBZ+a2triUMpYbtr8+bNwvHJT27fvj1hwgRyoYKNjQ33PBAHkiJP3nIvI2lEkUo8jcgWqaurU1FRMTMzYwZSFNWpUyeR6h1Zo7CwsBB+kcj0P336hBAaPnw4M7AJNUzuiliyZAm5XkJGRkbkJlKRfGWhInh6eiKEwsLC6JDg4GCE0Lx584QjE5OSdRJv7ty5CCHW6t/jx48RQtra2sz6Jytp+vr6ku4/JE3Gkj1ygWSbNm1YR3ZJJkXOepBjeywjAWP88uVLhJCqqipJiphJIk0CVkOQjIlcLouIiEAIycnJMU/LiyE1NXXLli3m5ubELvXx8WE+Jcv+zB2nWHL55C75jcKxisaNG4cQYh6XZSGVIkg0OHDvO2RHd0MHHMSIGc3AgQNlZGQ+f/7MDNy0aRMS2obNpKKigrhjoA9LM9/I6n0AAAAA8N0j8ZUwr1+/NjExaehpXFycrKws64JN4k+F6OIEPp//5s0bExMTssGJed9DXFxcQUHB4MGDma596+vr375926VLF/qmGYRQbW3t3bt3TU1N7e3t0T/bTRFCxBmGlZUVK9von3tWcnNzyV7ERhGZFPPKlsTERIFAgBAim9BoXbNpMFP+8uUL2ZxMNqkihIjHSxr8zwFUclaQQG4pUFBQmDBhwu3btzMzM7t06fL+/Xv6kgyOeaBbEP+zgQ1JUkbSiM7OzmIuRSQtQo6i0YSFhVVWVrICg4ODMzIyJk6cqKioiP85rUq4detWVVXV/PnzeTxeVVXVx48fxadP/JF4eHgghMrLy9PT05GENVxdXU1RFI/H69u378mTJ7OzsydNmkRRVEhISKPVQvjKQkUIDw9XVFRkXinMbOicnBz68hKKovz8/PT19ckeeEJdXZ2Pj4+RkRFZ24mLi2P2NUtLS2ZDx8XFFRYWktavrq4mR/64wJI9wu3btxFCc+bMoa+spDNpYGBgamoqnE5OTg5CyMLCghV+6dIlhNC0adNIUiQacSpDwxwoWIEi7w0mbWRqair+nkyBQECuLDIxMdm+fXtCQsIff/yBECLrhDRkP+e8efMQQtnZ2aRRJJJPJInkNwrHKmpUUKVSBIkGB459B2P8+vVrHR0dOmMZGRmlpaXkb/FiRkhNTfX39x81apSBgQFCiM5AQ0JIk52dTVGUnJwcM5P0G0nvY451AAAAAPB9I7FR6uvrW1BQIPJRaWnpmzdvli5dqqWlxQwnh2RsbGzokPDw8IqKCqLWJCUlkQ2NdPoIIRcXF2YKoaGhlZWVrMBXr16VlZV5eHgQg4Rs40QIkavYWYrU06dP0T+K1Nq1a4mD2UYRTqqmpsbf39/AwKBLly4Y48mTJ/P5fIQQsa5F6i4lJSVEQWkUpra3ZcsWcoVD+/btZWRk9PT06AvcCQEBAR8/frSxsSFHQBFCu3fvbtu2LXEQQmjXrt3o0aM1NTWJDypJ84AQ8vHx2b9/P/mbexlFWhcsRDa0yECy9ZTo04GBgcQ9D+H69esyMjIzZsxACHl7ez969Eh8Unfu3FFQUCBuWk6ePPnixQskSQ2/ePFCV1eXLK0Q5OTkyNuJSsqFryxUCKHa2trk5GRLS0um4cQ0tFavXk2bjrGxsbRJyYxcUlJCXImS+yeJjdFoX7t69er169c55pM02cCBA+kQjPGdO3fU1NS2bdvGjCkykzR6enpIyCCpqqq6ffu2iooKWZpDCLVr1w4hxLwVtry8/NWrV6QhhDMmUp7FtBFFUUlJSQihvLy8Ll26GBsbk7kGhBCPxyPjFVNs6urq7ty507179549eyKEVq1aRXxxc5dPZm65SH6jcKwiMZWQmppaW1srlSJINDhw7DuJiYl5eXm0IFEU5e7u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3tpPPCQk5MuXLyLWClu/fj1C6Ndff23Vu75/Hz588PX1JUny9evXCKFNmzbNnTs3ISGByjBx4kQ5Obni4mLJ1ZEkSZK6Dyhw6gMAAADaT6uDUl9fX4RQUFAQPXHatGkIoQMHDoivYv8Hh8Pp2bNnp06dMjMzqUSCIPT09BBCrbro/wFIpDVaDEpxT92NGzfS6ykjI6OiosJmswUyCwelERERDAZD+L7GihUrEEJRUVEkSW7fvl1XV5ce9ZEkSRCEqampKLvAZrMtLS0RQs+ePRN4aeLEiQghgaCUJMnOnTsLX5lVVVUJBKUEQbi6uiKEEhMT6TnLy8sZDIarq6so1SNJ8vLlywih1atX0xNPnz6NEBo/fryIhXSYmpqaXr16GbVSt27dBKI1YSNGjKiuriZJct68eQihcePG4bDtw4cPCgoKdnZ2VVVVVGYJNtrmzZsRQosXLxZIr6ioUFFRkZeX//jxI5U4adIkhNDAgQPpOYcOHYoQevv2rUAJQ4YMkZGRwU96SZKMiIj4448/SkpK8L9Hjx5FCElLS1P3pKjKUIFri7y8vAoKCkiS/PLlC0Jo1KhRorxrypQprf3EjYyM5s6dK2KtsB81KN2xY8fz589Jkrxy5QpCSFVVlX53jCTJ5cuXI4RCQ0MlVMH/D4JSAAAAHa91Y0ojIiLOnTs3bNiw8ePH09PxZfrIkSMbfVdSUlJycvKMGTNatS26Q4cOffjwYcuWLfSBT3w+v6amRl1dvXfv3gL5ExMTw8LCSkpKzMzMnJ2dtbS0vnnT36HWtkbHmD9//r1793BshsnJyRkbG3/8+LGkpERfX7/5t/v7+5MkOWTIEIH0ESNGBAYGPnjwoG/fvkwm8+vXr6tWrfrtt9+oz5TBYKxevVqUGu7bty8lJaV///4CHY8RQt7e3nfv3hV+i6ysrHAifnxK9+rVq8ePHzOZTCsrK3q6hoaGjY3NkydP2Gx2izNbVlVVrVmzRlFRcevWrQLpqIkvF0mSN2/etLS0xMF2W5Akef/+/S5dugwYMEDEt6ioqKSkpLRxu8JKSko0NTXxE9H4+HiE0O7du/FoSXNz87KyMkVFRWrwpGQbDVfjl19+EUhXV1f39fU9fPjw6tWrHz16hBOnTp2amJgocBq0sLAICwvLyMgQaHYpKSkej+fo6Ij/7d+/f//+/alXR40a1atXrz59+uB1O6iiEEIZGRmi1LysrIzD4ejq6iKEbty4gRAS/lI0CmcG3yYiIgLH2/jA9vf3x58aBX98wiONAQAAgB9eK4JSgiD8/PwQQl5eXvR0Ho8XFhamoaFhbW1NTw8PD4+Li3v//v2lS5eGDBnyzUFpfn4+7sUnMJlNfHx8dXW1h4cHfYIfgiDWrFmjoKDg6urKYDDOnj27dOnSffv2LViw4Nu2/r1pVWt0pICAgICAAPw3m83Oy8srKiri8XgIoaqqquaDUj6fj8esmpqaslgs+kt42o+0tDSE0KRJk3bu3Hn48OEjR47gQa3Dhw8fOXKkiB/utWvXEELDhg0Tng9GOK7ARJw5JjIyEiHUq1cvgfGBCCF9ff2EhISMjIxevXo1X8gff/xRVFQ0efJkZWVlevq///6LEBoxYoTwW5KTk729vTdv3txMfPXx40dzc/OmXiVJ8u7du2lpaZGRkUFBQdu3bxc9KG0nampq+ElgTU1NUlKSvr4+/cJdSUmJnrmdGq3tBg0adPjw4bCwMIIg8F0MT09PT09P/Cqfz8/Pzy8qKiopKUH/C6GFmZmZNZVOvx1QVFRUWFiYnp7eTFECVFVVT548iRAiSfKvv/6SkpJqy01DIKITJ07glW9w990pU6bQX+Xz+W/fvu3SpUuL03RxudyAgADhkdXN6NSpk7+/v/ANNQAAAOA70YqgNDY2Nj4+XkpKCvdDo8TExNTU1EyYMEHgB6+qqqpHjx5z5sx58uRJW6p49erV2traXr16CVzWv3z5Egldd544ccLOzo66wBo4cGBtbe2iRYu6d+8+atSotlTjO9Gq1uhgFRUVV65cefLkSX19vbm5uaWlJV7XlGxpspnPnz/jDmN3794NDQ0VeHX16tV4TJ2ent7z58/9/PzCw8NjYmJiYmICAgKsra3Pnj2LMzSDIAh81W5iYiL8ahuv1ZKSkhBC5eXlf/zxh8BLpqam69ata3FGzYaGhvPnzyOhOz5cLjcsLExTU1PgGSxmYWHx/PlzPGNwUwYMGIC7XjeKJMnq6uqBAwd6eHgEBQU1X8mOIScn16VLF4RQeHg4n88fMWJEU7cG2q/R2s7Y2BghVFNTk5GRQR1yPB7v9u3bjx49womWlpYcDgc1/QXB7dCUsLCwO3fuREVF6enpWVpa4rs5LX7XMKqRIyMj09LSXF1dBab2Be0BR5vV1dVxcXGGhoYC98KioqIqKio8PDxavBdGkmR9fT19IvQW4TEU31BnAAAAoGO0IigNCQlBCPXs2VNHR4eejh9KCPeUw+sZtB3e7vDhwwXSG93ulStXCIJwcXHBQxwZDMbChQv//vvv8+fP/xhBaatao13xeDySJKkOrkFBQb6+vtra2kePHqWqceHCBVGKwrErQmjZsmW2trbN5LS2tn716tXHjx/fvn376tWroKCgd+/ejRkzJikpqfnHCwwGQ0VFpbKysj2eJOP6m5mZUfP3tlZCQgJ+7iHwyUZHR9fW1jo7OzcaNsvIyLTY65LL5TbzqpSU1Jw5cxBCnz9/bm2d21tThzql/Rqt7XAfAYQQNTzv06dPXl5eOTk5e/bsuXjxIj4Oi4uLqf69jVa10XQWi+Xj43Pv3r01a9YEBwfjZYcePXp08ODB1tbzr7/+QgjNnj27tW8E3wzfbXF0dBQIPm/evIkQ8vDwaLEEOTk5qlsKAAAA8GNoRVCal5eHEBLu80Z/RldRUSElJfVtazO2artsNvv169edO3fGDwyzsrKMjIwYDAaPx4uPj2exWNQKmXj6nw8fPoixShLUqtZo15rcv3+fxWLhy9moqChPT09VVdXg4OCmeurW19fTh8DRdevWTUFBgc1ml5WVNbPFixcvjhgxwtDQsGfPnj179vT19eVwOFu2bNmzZ8/p06dxr+amMBgMW1tbPBGoqHvYBOEHFD179kQINV/55uGPVUdHR2D8M/3LxefzCwoKvp9lS1kslpOTk0B36xYxGIxVq1bhSLh5OCgdNmxYUxm+50bDHc7l5OTw07Dq6monJ6e8vLzHjx8LL2+L4YnBRLlpMn369KCgIH9//6YiEx6PRxAEtQxmU+rr62/cuKGuro7nCCgpKVFQUMCjeZsyZ84c+so0Iho+fPixY8da+64fVaN3W3g83s2bNxUUFCZMmIAQqq6u5nK537DOMwAAAPAf1YqgVF1dHSEk0GuUxWK9fftWQ0MDj/sKDAz08vISb1Da6HZfv37NZrNdXFxw6LV+/frr168zGIznz5+Xl5fjxVEwfHVoamoqxipJUKtaIyoq6tKlSzk5OYsWLXJ2dj5w4EBBQUFlZWVOTs6xY8cE5thoHn7oxOfzqRQej0ddQB88eJDL5c6fP18gIi0uLqb+9vb2bmotREVFRU9PzytXrsTExAg/xeJwOJcuXZo/f35CQkJ5efnKlSupl+Tl5QMCAq5du5adnd3iLowcOTIkJOTNmzfCL9HrKVAx4UThuWSmTp26c+fOpKSkhoYG4Ujg3r17ffv2xTdHmtLox4oQwqvO4vmfwsLCUlNTly5dihB68OBBdHR0aGjoxo0bx44d20zJ7UdZWTkgIKC2trZV72IwGPb29i1mq6ysTEhIEO7iSPedNFqjvSLDw8MRQh4eHioqKgihq1ev5uXl9evXTyAipR9427dvnzp1aosjXT98+BAUFCQlJfXbb781VVRoaOjHjx/xFADNePnyZXV19eLFi/EsXBs2bFi7dm1TA1mxlStX5uTkNF+ssGY+xJ9Qo3db/v3336KiIk9PTyaTiRA6cOCAo6MjnpwZAAAA+CmIPlEv7ly0fft2euKGDRsQQsOGDSP/tzCG8MKAenp6jo6OTRW7detWIyOjP//8s6kMixcvRgiFh4dTKQ0NDfiKc8uWLSRJ5ufn48XfGuXu7s5gMAQWXeBwOBMmTDA2No6IiGjqjSRJ/vPPP+bm5gKrTQjgcrmenp42Njbx8fFtLIoUd2vMmjWLz+evXbu2c+fO8+bNi4yMxOnjxo3DH5noCIJQUlJiMBjU+i779+9/8eIF/hv31z127Bj9Lfn5+fgYe/fuHUmSEyZMoF7CF6n0Q6WoqEhLS6t79+719fUCm969e/fRo0dJkvz1119tbW1xt2G6wYMH79ixo8VdqKurw6P7BBZuIUly4cKFqLElYfDTNvriqyRJ/v777wwGQ0NDg564ZcsWhNDp06cFSqisrLSzsxNeFEdAQUEBg8EQ+JoEBwcjhGRkZDgcDkmSixYtysrKIkkyPj4eL73j7e1tY2PTfMnKysrNZ8DwgFuBb7cEPXjwACE0Z86cZvKIsdHYbPawYcOMjY2p74go8Ic+f/58gfTc3Fw5OTlNTc2vX7/iFLySqqenJz0bQRB4DqojR46QJLl+/Xpq8WccjeTk5AhvNCwsDCGkpaUlkI6PYbyo75MnT1pcd4ckSTxDGD43FhQUODk5ibLXHWDdunUIoeXLlzeVocXzJEmSGRkZ/fv3HzNmDF5eqCm7du0yNTW9cuVKM3lEPMnfv3/f1NR07ty5AstW0eFlogwNDQXS8S8pXvCWxWINHDiwmULaGzVhW3l5eaMZRGxbAAAAQHStCEobGhpMTEycnZ3xvwRBbN68edmyZXjmRpIko6KiVq5cKfzGZoJSLpcrLy+PEFJSUqqpqWk0T1pamoyMzO7du/G/eFIlfAV29uxZkiT37Nnz4MGDRt+LL23PnDkjkI6fY1DhdFNGjx6Ns5WVlTWV5+3btzhPM5dQIhYl3tZITk7eu3cvSZITJkxgMBj0te88PDx69OjRTG0bhXvqBgcH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[wxMaxima: image end ] */
/* [wxMaxima: section start ]
Maxima es capaz de obtener la fórmula, si lo vamos dirigiendo
[wxMaxima: section end ] */
/* [wxMaxima: comment start ]
Le decimos la fórmula del término general a(n)
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
a(n) := a*r^(n-1);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
Le pedimos que haga la suma de a(1)+a(2)+...+a(n);
o sea la suma de a(k) cuando k va tomando los valores desde 1 hasta n.
Y se limita a escribirla; parece no saber hacer la suma.
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
sum( a(k), k,1,n );
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
Si le hubíeramos dado un valor concreto para: a, r y n
habría obtenido la suma de forma inmediata... pero con letras es más delicado.
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
sum( 3*(1/2)^k, k, 1, 100);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
Le decimos que carge una librería adicional destinada a simplificar sumas "con letras"
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
load(simplify_sum);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
Le decimos de nuevo que haga la suma, y que simplifique el resultado
con ayuda de la librería que hemos cargado
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
sum( a(k), k,1,n );
simplify_sum( % ); /* Que simplifique el resultado obtenido */
fullratsimp(%); /* Que simplifique la función racional resultante */
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
MAXIMA HA SIDO CAPAZ DE OBTENER LA FÓRMULA QUE NOS HABÍAN PROPORCIONADO.
PERO... CUIDADO: ¿QUÉ PASA SI r=1?
[wxMaxima: comment end ] */
/* [wxMaxima: section start ]
Aplicamos el método de inducción para demostrar la fórmula
[wxMaxima: section end ] */
/* [wxMaxima: subsect start ]
Comprobamos que la fórmula vale para n=1
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
sum(a*r^(k-1), k, 1,1);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
'sum(a*r^(k-1), k, 1,1) = sum(a*r^(k-1), k, 1,1);
/* [wxMaxima: input end ] */
/* [wxMaxima: subsect start ]
Supuesto que la fórmula vale para n se trata de comprobarla para n+1
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
print("Suponemos que ")$
'sum(a*r^(k-1), k, 1,n) =(a*r^n-a)/(r-1);
print("y sumamos un término más")$
(a*r^n-a)/(r-1)+ a*r^n;
print("simplificamos el resultado para comprobar si es lo que esperábamos")$
fullratsimp( (a*r^n-a)/(r-1)+ a*r^n );
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
JUSTO LO QUE ESPERÁBAMOS. OBJETIVO CONSEGUIDO
[wxMaxima: comment end ] */
/* [wxMaxima: title start ]
Un reto
[wxMaxima: title end ] */
/* [wxMaxima: caption start ]
[wxMaxima: caption end ] */
/* [wxMaxima: image start ]
png
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
[wxMaxima: image end ] */
/* Old versions of Maxima abort on loading files that end in a comment. */
"Created with wxMaxima 22.04.0"$