Fixed small descriptive error in taylor series

book/knowledge-library/monovariable-calculus.ipynb

@@ -2393,7 +2393,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "T^{(n)} = c_n (n)(n-1)(n-2)\\dots(3)(2)(1) (x-a)^{n -n}\n",
+    "c_n (n)(n-1)(n-2)\\dots(3)(2)(1) (x-a)^{n -n}\n",
     "$$"
    ]
   },
@@ -2402,7 +2402,7 @@
    "id": "5cf39fa0",
    "metadata": {},
    "source": [
-    "Here we can write $n(n - 1)(n-2)(n-3) \\dots (3)(2)(1)$ as $n!$, $n-n = 0$, and anything raised to the power of zero is just one, so we get this expression for the nth-derivative of $T$:"
+    "Here we can write $n(n - 1)(n-2)(n-3) \\dots (3)(2)(1)$ as $n!$ (we call that \"n-factorial\"). For example, $3! = 3 \\times 2 \\times 1 = 6$. We can also rewrite $n-n = 0$, and anything raised to the power of zero is just one, so we get this expression for the nth-derivative of $T$:"
    ]
   },
   {
@@ -2411,7 +2411,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "T^{(n)} = c_n n!\n",
+    "c_n n!\n",
     "$$"
    ]
   },
@@ -2474,7 +2474,7 @@
    "id": "ac889c4c",
    "metadata": {},
    "source": [
-    "This is the formula for the **Taylor series** of a function. For practical purposes, we usually don't let the sum range from 0 to infinity, and instead cap the sum at some number, which we call the **order** of the resulting polynomial. For example, the 7th-order Taylor polynomial is a Taylor series with 7 terms."
+    "This is the formula for the **Taylor series** of a function. For practical purposes, we usually don't let the sum range from 0 to infinity, and instead cap the sum at some number, which we call the **order** of the resulting polynomial. For example, the 7th-order Taylor polynomial is a Taylor series capped at 7 terms."
    ]
   },
   {