Polynomial convergence question.

[rcmango]

Homework Statement

To find convergence, why can't I divided by the largest n in the denominator in this problem: SUM n_infinity 1/(n^2 - 4n + 4) ?

its suggested to use the comparison test.

(I think SUM stands for E Reimann sum correct?)

but in this problem, I can easily find convergence by dividing by large n in the denominator: lim n->infinity 3n^2/(7n^2 + 1)

?

any explanation please. thanks.

Homework Equations

The Attempt at a Solution

its all above. thanks.

 

[Dick]

Basically, because one is a limit and one is a sum.

 

[rcmango]

Okay, so for a limit, its okay to divide by the largest N, but for a sum it is not common?

 

[HallsofIvy]

Do you understand why dividing by the largest power of N, in both numerator and denominator helps you find the limit of a sequence? Would that apply to an infinite sum?