Let . Which statement about is…

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

Problem

Let

S=\displaystyle\sum_{n=0}^{\infty} 12(-1.2)^{n}

. Which statement about

S

is true? (a)

S

converges because the negative common ratio makes successive terms cancel. (b)

S

converges to

\displaystyle \frac{12}{1-(-1.2)} \approx 5.5

. (c)

S

diverges because the common ratio has magnitude greater than

1

. (d)

S

converges conditionally but not absolutely since the series is alternating.