Question

DIVERGENCE TEST

Answer 1

do you have to use the divergence test?

Answer 2

yeah

Answer 3

ok so we need to show
\[\lim_{n \rightarrow \infty} \frac{(-1)^{n+1}n^2}{2n+1} \neq 0\]
in order to use the divergence test

Answer 4

ok

Answer 5

so we must show that limit there either doesn't exist or is some value other than 0 to show that series in question is divergent

Answer 6

its undefined

Answer 7

that sounds good to me n^2/(2n+1) was already getting really really big
throwing in the (-1)^(n+1) is just going to alternate the signs of these big numbers

Answer 8

so from that we are done

Answer 9

we have shown the limit isn't 0