Doesn't the second one diverge by Nth term/TFD or am I mistaken?
show that the sum of 1-cos(pie/n) from n = 1 to infinity converges or diverges
second question:
show that the sum of e^-n/(n+1) from n =1 to infinity converges or diverges
i think it converges. is it okay if i use the comparison test by comparing series to another series and can i use the integral test to see if series being compared converges?
#1: We're going to make use of the fact that for all , we have: . To prove this, consider and prove that it is a decreasing function. Thus,
So now we have the inequality: since for all .
Now use comparison.
#2: Use the divergence test. If is not equal to 0, then the series diverges.