If $a_{n}>a_{n+1}>0$ (For All N)and $\sum a_{n}$ Converges, Then $\sum(-1)^{n} a_{n}$ Converges

True/False

If $a_{n}>a_{n+1}>0$ (for all n)and $\sum a_{n}$ converges, then $\sum(-1)^{n} a_{n}$ converges.