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GRE - Quantitative Reasoning - Sequences and series

In the sequence a1, a2, a3,....a100, the kth term is defined as ak= 1/k - 1/k+1 for all integers k from 1 through 100. What is the sum of 100 terms of the sequence?

In the sequence a1, a2, a3,....a100, the kth term is defined as ak= 1/k - 1/k 1 for all integers k from 1 through 100. What is the sum of 100 terms of the sequence?

A. 1/10100
B. 1/100
C. 1/101
D. 100/101
E. 1

ak = 1/k - 1/(k+1)

a1 = 1/1 - 1/2

a2 = 1/2 - 1/3

a3 = 1/3 - 1/4

.

.

a100 = 1/100 - 1/101

Adding them up

the terms 1/2, 1/3 . . . 1/100 get cancelled

Sum = 1 - 1/101 = 100/101

Option D is correct