Let an AP with positive first term and positive common difference and a GP with the…

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let an AP with positive first term

a

and positive common difference

d

and a GP with the same first term

a

and common ratio

r>1

be given. (i) Prove that there can be at most one positive integer

n

for which the sums of the first

n

terms of the two progressions are equal. (ii) If such an integer

n_0

exists, prove that for every

n>n_0

the sum of the GP exceeds the sum of the AP.