Question

How to show (n+i)/(3n^2+2i) is divergent?

Answer 1

\[\sum_{n=0}^{\infty} \frac{ n+i }{ 3n^2+2i } \]

Answer 2

i take it \(i\) is some sort of constant?

Answer 3

imaginary number?

Answer 4

it is divergent because the denominator is a polynomial of degree 2 and the numerator is a polynomial of degree 1 and \(2-1=1\)

Answer 5

How can I prove it, got any tests I can use?

Answer 6

the degree of the denominator must be greater than one more than the degree of the numerator

Answer 7

you can arrange it so you can compare \(\sum\frac{1}{n}\) which is well known to diverge

Answer 8

but why does 1/n diverge? if you take the lim to infinity doesn't it go to 0?