As you may have guessed, I am currently studying cal II, the section about: sequences, series, power series, et al...

I do not understand the need for representing functions as power series? I know how to mechanically find the answer (following procedure basically) but I lack the understanding behind it.

Can someone please explain it to me with some clear examples.

So what if I knew that $\displaystyle \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n$?

Is that saying:

When x = 3 then:

$\displaystyle f(3) = \frac{1}{-2} = \sum_{n=0}^{\infty}3^n$

I am lost....