Originally Posted by

**blitze105** Hello all,

Unfortunately I was absent during one of my classes this week when the professor covered Taylor Series. i have gone through the book and finished all of the first section of the homework. The second section, however, is not in my book... and I can't find it online.

If any one could help me find examples on these types of problems or simply point me in the right direction I would greatly appreciate it. I am NOT asking for answers.

1) Find an expression for the general term of each of the series below. Use n as your index, and pick your general term so that the sum giving the series starts with n=0.

$\displaystyle x^4\sin x^2 = x^6 - \dfrac{x^{10}}{3!} + \dfrac{x^{14}}{5!} - \dfrac{x^{18}}{7!} +\ldots$

2)find the sum of each convergent series.

$\displaystyle 1- \dfrac{2^2}{2!} +\dfrac{2^4}{4!} - \dfrac{2^6}{6!} + \ldots + \dfrac{(-1)^n2^{2n}}{(2n)!} + \ldots$