The least value of in order that the sum of first terms of the infinite series

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The least value of nn in order that the sum of first nn terms of the infinite series 1+34+(34)2+(34)3+…1 + \frac{3}{4} + \left(\frac{3}{4}\right)^2 + \left(\frac{3}{4}\right)^3 + \dots , should differ from the sum of the series by less than 10−610^{-6} , is (given, log⁡2=0.30103,log⁡3=0.47712\log 2 = 0.30103, \log 3 = 0.47712 ) (1) 14 (2) 27 (3) 53 (4) 57

Related theory

Browse the problem library