Question

True or false?

Answer 1

If \[\sum_{n=1}^{\infty} (-1)^{n} a_{n}\] converges, then \[\sum_{n=1}^{\infty} (-1)^{n+1} a_{n}\] converges.

Answer 2

\[\sum_{n=1}^{\infty} (-1)^n a_{n}=-a_1+a_2-a_3+...\]\[\sum_{n=1}^{\infty} (-1)^{n+1} a_{n}=a_1-a_2+a_3-...=-\sum_{n=1}^{\infty} (-1)^n a_{n}\]

Answer 3

so I'd say true