I was asked to find sums equal to 9/25 by using the power series of $$y=\frac{1}{1+x^2}$$. First thing I did was to find the power series representation of the function:
$$\sum_{n=0}^{\infty }(-x^2)^n$$
Next I figured out the interval of convergence:
$$\left \| -x^2 \right \|< 1$$
This...
How would I find the interval of convergence for the following series:
i) $$\sum \frac{(x+2)^n}{n^2}$$
ii) $$\sum \frac{(-1)^kk^3}{3^k}(x-1)^{k+1}$$
iii) $$\sum (1+\frac{1}{n})^nx^n$$
Reason for edit: My second series was not displaying properly