Question

Determine whether the following series converges or diverge.
SUM (3n^3+5n+1)/(7n^5-6n^2-3) n=1 to inf

Answer 1

I took this limit and I got lim n->inf of 3/7n^2 = 0. But I was told that is not enough to guarantee convergence.

Answer 2

do it with your eyeballs
degree of numerator is 3
degree of denominator is 7
7- 3 = 4 and 4 > 1 so it converges

Answer 3

it is not that the limit is zero, but rather that it goes to zero "fast enough" that is it goes to zero as fast as \(\frac{1}{n^4}\)

Answer 4

The degree of the number is 3, but the denominator degree is 5. 5-3 = 2 which is still > 1. I see, Thanks. Second time today lol.