Find the power series representation for the function, and the interval of convergence.

$\displaystyle f(x) = \dfrac{1}{1 + x} = \dfrac{1}{1 - (-x)} = $ Summation sign goes here - n = 0 to infinity$\displaystyle (-x)^{n}$ ??? Why is there an "n" power here over $\displaystyle (-x)$ ??

Summation sign goes here - n = 0 to infinity $\displaystyle (-1)^{n} x^{n}$ ??? What is going on here?

$\displaystyle |-x| < 1$

$\displaystyle |x| < 1$

$\displaystyle R = 1$ ??

$\displaystyle I = (-1,1)$