Question

On finding the interval of convergence for a power series I need help testing an endpoint. x= -1 for (1/n2^n)*(x-1)^n which when plugged in would be -2^n/n2^n ....using alternating series test, please show work and explain as you go.

Answer 1

need someone to double check this but \[\sum\frac{ -2^n }{ n2^n } \] would be this \[\sum 1/n\] and using the AST the lim =0 and 1/n is greater than 1/(n+1) ....right?

Answer 2

\[\large \sum_{n=0}^{+\infty}\frac{ (-2)^n }{ n 2^n }=\sum_{n=0}^{+\infty}(-1)^n\frac{2^n}{n 2^n}\]