Question

Does lim(n-->inf) Un=0 imply that Sum of Un converges as n-->inf?

Answer 1

Yes, I think it does. Let me check a little more.

Answer 2

pls provide a egsample

Answer 3

And also the following condition must be satisfied, Un-1> Un>Un+1, which means if you find one of the terms to be zero when n is very very large but the trend is not getting smaller with n getting larger then the series in not converging.

Please refer to the site http://www.math.unh.edu/~jjp/radius/radius.html

Answer 4

U mean the function shud ebe decreasing .. right? if there any his shud be divergen? any egsamples

Answer 5

are you asking "if the terms go to zero, then does the sum converge?"
if so the answer is no emphatically no

Answer 6

canconical example is
\[\sum\frac{1}{n}\] the well known divergent harmonic series

Answer 7

Thanks dude...

Answer 8

yw