Question

series converge or diverge

Answer 1

see questions attached. Please show all steps.

Answer 2

@jim_thompson5910

Answer 3

@satellite73 please help

Answer 4

\[\sum_{n=3}^\infty (-1)^{n+1}\frac{1}{n(n-2)}\]
An alternating series; apply the alternating series test.
\[\text{Is }\frac{1}{n(n-2)}\text{ a decreasing sequence? (show that it is)}\\
\lim_{n\to\infty}\frac{1}{n(n-2)}=0~?\]
Test for absolute convergence; does \(\displaystyle\sum_{n=3}^\infty \frac{1}{n(n-2)}\) converge? (hint: is it a telescoping series?)