Let . Consider the geometric progression with first term and common ratio . Which…

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

Problem

Let

0<r<1

and

a>0

. Consider the geometric progression with first term

a

and common ratio

r

. Which statement about the partial sums

S_n

(sum of first

n

terms) is always true? (a)

S_n

decreases with

n

and tends to

0

. (b)

S_n

increases with

n

but never exceeds

\dfrac{a}{1-r}

. (c)

S_n

increases with

n

and eventually equals

\dfrac{a}{1-r}

for some finite

n

. (d)

S_n

increases without any upper bound.