Register to reply

Infinite Series: sigma n^2/(n^2 +1)

by anderma8
Tags: infinite, n2 or n2, series, sigma
Share this thread:
Apr24-07, 11:29 PM
P: 35
If I take the limit on the sum... I get 1/1 = 1

If the limit does NOT = 0 then sigma f(x) diverges...I'm not quite sure I follow this... Does this mean that in order for the equation to converge, the sum (sigma) must be = to 0?
Phys.Org News Partner Science news on
Flapping baby birds give clues to origin of flight
Prions can trigger 'stuck' wine fermentations, researchers find
Socially-assistive robots help kids with autism learn by providing personalized prompts
Apr24-07, 11:49 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,771
You're again confusing the limit of the argument (here n^2/(n^2 +1)) with the actual sum, which is the limit of


as N-->infty.

The theorem is saying that if the limit of the argument is not 0, then you must conclude that the sum diverges. If it IS 0, then you cannot conclude anything: the sum could converge or diverge.

For instance, consider the old harmonic series


Sure, 1/n-->0 but it is well known that the harmonic series diverges nonetheless.

Register to reply

Related Discussions
Infinite Series: sigma (2^n)+1/(2^n+1) Calculus 7
Infinite sigma-algebra Set Theory, Logic, Probability, Statistics 3
Countably infinite sigma-algebra Set Theory, Logic, Probability, Statistics 1
Infinite sheet of charge..just need help on sigma stuff Introductory Physics Homework 3
Pi-Sigma hybrid series Linear & Abstract Algebra 0