Which of the following series is both geometric and convergent?

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

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

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

(b)

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

(c)

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

(d)

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