calculus
posted by sarah
determine whether the series converges of diverges
the sum from k=1 to infinity of
cos(e^k)
I'm not sure where to start..

drwls
As k becomes very large, e^k approaches zero, and every cos(e^k) term approaches 1.
You end up with an infinite series of terms all approaching +1, which cannot converge
Respond to this Question
Similar Questions

Calculus
The problem with these two questions is that I cannot determine the a and r. The 3rd questionI don't know what I did wrong. Thanks for the help! Tell whether the series converges or diverges. If it converges, give its sum. infinity … 
calculus
determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges 
calculus
determine whether the series converges of diverges the sum from k=2 to infinity of (the square root of (ln(k)))/k I said that because you can't integrate the series (goes to infinity) it diverges 
calculus
determine whether the series converges of diverges the sum from n=1 to infinity of sin(e^k) I'm not sure where to start.. 
calculus
determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges is this true? 
calculus
determine whether the series converges of diverges the sum from k=2 to infinity of (the square root of (ln(k)))/k I said that because you can't integrate the series (goes to infinity) it diverges is this true? 
calculus
determine whether the series converges of diverges the sum from k=1 to infinity of sin(e^k) I'm not sure where to start.. 
calculus
determine whether the series converges of diverges the sum from k=1 to infinity of sin(e^k) I'm not sure where to start.. 
Calculus 2
I need help in solving an initialvalue problem and a few series problems (Especially on #45 & #46). I don't really understand how to do the series problems...majority of the time. An explanation would be great as well. Thank you for … 
Calculus
Determine whether the series from 0 to infinity of cos(nπ)/(n + 3) converges conditionally or absolutely. A. The series diverges. B. The series converges conditionally but not absolutely. C. The series converges absolutely but not …