Consider an infinite G.P

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

Problem

Consider an infinite G.P. with positive first term

a

and common ratio

r=-\dfrac13

. Let

R_n

be the remainder after the first

n

terms are summed. What is the sign of

R_n

when (i)

n

is even and (ii)

n

is odd? (a) Positive for both even and odd

n

(b) Positive for even

n

and negative for odd

n

n

and positive for odd

n

(d) Negative for both even and odd

n