Mathematics

Mathematics

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.

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