Domain of the function

[pka]

The function [imath]f(x)=1-x+x^2-x^3+\cdots+(-1)^nx^n\cdots[/imath] is the alternating series:
[imath]\displaystyle f(x) = \sum\limits_{k = 0}^\infty {{{( - x)}^k}}[/imath] which converges for [imath]|x|<1[/imath]. SEE HERE

 

[Loki123]

I will repeat: In order to help you, we need to know what you have learned about this topic.

If you have never heard of convergence, then this problem is not for you.

If you need to learn everything on this test even though it is not in your curriculum, then why have you not searched for lessons on convergence, geometric series, and other terms that have been mentioned, so you can learn it? We can't teach you everything from scratch; we are here to help you with what you are learning elsewhere.

Okay thanks! I'll come back to this when I learn more.

 

[Steven G]

A series converges if the sum of the series approaches a real number.
A series diverges if the sum is +/- infinity or the sum does not approach a single number (eg: 1-1+1-1+1-1+....)