What is the value of 1 + 1/4 + 1/16 + 1/64 + ... ? A. 2 B. 7/4 C. 3/2 D. 4/3

GATE 2018 · General Aptitude · Number Series · medium

Answer: S = 4/3 (Option D)

1. Identify first term and common ratio: a = 1 (first term). r = (1/4)/1 = 1/4 (ratio of consecutive terms). |r| = 1/4 < 1, so the series converges.
2. Apply the infinite geometric series formula: S = 1/(1 - 1/4) = 1/(3/4) = 4/3.