Mathematics

Problem

Which of the following series is both geometric and convergent? a)

\displaystyle \sum_{n=1}^{\infty} \dfrac{1}{n^{2}}

\displaystyle \sum_{n=1}^{\infty} \dfrac{n}{3^{n}}

\displaystyle \sum_{n=0}^{\infty} \left(-\dfrac{1}{2}\right)^{n}

\displaystyle \sum_{n=0}^{\infty} 5^{n}