simple question on limits

Question

I am getting skeptical about a simple question. It may seem dumb, so I am sorry in advance.

Is the following statement "always" true?

If $\displaystyle{\lim_{i \to \infty}} a_i=0$, then $\displaystyle{\lim_{i \to \infty}} (-1)^ia_i=0$, where $a_i$ are real.

Thanks.

Answer 1

HINT

$|(-1)^ia_i|\leq |a_i|\to 0$