I have the following alternating series $1+1/2+1/2-1/2^2+1/3-1/2^3+1/4-1/2^4$ does the alternating series converge or diverge?does the alternating series apply?
I know that the series can be written as $1/n-1/2^n$ which as I can see not alternating, so the alternating test is not applicable $1/n>1/2^n$for all n, but how can I prove that it converges.