# Polynomial convergence question.

1. Apr 15, 2007

### rcmango

1. The problem statement, all variables and given/known data

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)

?

2. Relevant equations

3. The attempt at a solution

its all above. thanks.

2. Apr 15, 2007

### Dick

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

3. Apr 15, 2007

### rcmango

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

4. Apr 16, 2007

### 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?