Problem 1105 (difficulty: 4/10)

Assume that \(\displaystyle a_n\le b_n\le c_n\) for all positive integer \(\displaystyle n\). Show that if \(\displaystyle \sum\limits_{n=1}^\infty a_n\) and \(\displaystyle \sum\limits_{n=1}^\infty c_n\) are convergent, then \(\displaystyle \sum\limits_{n=1}^\infty b_n\) is also convergent.

Give me another random problem!