Problem 1100 (difficulty: 4/10)

True or False?

(a) If \(\displaystyle a_n\to0\), then \(\displaystyle \sum\limits_{n=1}^\infty a_n\) is convergent.

(b) If \(\displaystyle a_n\to0\) and the partial sums \(\displaystyle \sum\limits_{n=1}^\infty a_n\) are bounded, then \(\displaystyle \sum\limits_{n=1}^\infty a_n\) is convergent.

(c) If \(\displaystyle \sum\limits_{n=1}^\infty a_n\) is convergent, then \(\displaystyle a_n\to0\).

Give me another random problem!