Sequences, Series  CAT 2016 Math Preparation
Question 4 the day : February 14, 2003
The question for the day is a sample practice problem in sequences, series  geometric progression. Introduces concepts in GP summation, common ratio.
Question
Given A = 2 ^{65}
and B = (2 ^{64}+2 ^{63}+2 ^{62}+...+2 ^{0})
 B is 2^{64} larger than A
 A and B are equal
 B is larger than A by 1
 A is larger than B by 1
Correct Answer is A is larger than B by 1. Correct Choice is (4)
Explanatory Answer
B is in G.P. with a = 2 ^{0}, r = 2, n = 65
S _{n} =
B = 2 ^{65}  1
=> B = A  1
A is larger than B by 1
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