Question

ratio test

Answer 1

Tried to work this problem out! I am getting diverges but my book says converges. help ? :/

Answer 2

Show what you tried, and we'll help! It's probably just a small fix. =)

Answer 3

ok let me try! give me a min :)

Answer 4

\(\lim_{k\rightarrow \infty}|\frac{\frac{2^{k+1}}{(k+1)!}}{\frac{2^k}{k!}}|=\lim_{k\rightarrow\infty}\frac{2^{k+1}}{(k+1)k!}\frac{k!}{2^k}=\lim_{k\rightarrow\infty}\frac{2}{k+1}=0<1\)

thus it is absolutely convergent and thus convergent

Answer 5

@zzr0ck3r you beat me to it! i totally see what i did. at the end limit of (2/k+1) i thought that went to infinity -_- but i see that its infinity over a constant so its zero :)

Answer 6

It's actually a constant over infinity.

Answer 7

other way around

its a constant over infinity

Answer 8

oops yes i meant to say that! my bad. but i understand. thank you for taking the time to answer that for me :)