Let with . After multiplying by and subtracting, what is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

S_n = a + ar + ar^2 + \dots + ar^{n-1}

with

r \neq 1

. After multiplying by

r

and subtracting, what is

S_n - rS_n

equal to? (a)

a(r^{n}-1)

(b)

a(1-r^{n-1})

(c)

a(1-r^{n})

(d)

ar(1-r^{n-1})