Thread: Power Series Problem - # 2

1. Power Series Problem - # 2

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

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

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

$|-x| < 1$

$|x| < 1$

$R = 1$ ??

$I = (-1,1)$

2. Re: Power Series Problem - # 2

It's always based on 1/(1-x) = sum (n=0 ~ inf.) x^n. Now we are just replacing x with -x.
If you don't think it's making sense, it's because this only works if |x| < 1.
By the way, I tried with x=0.6, and playing with the first 10 terms did give me something near 0.625. xD