The sequence \(a_1, a_2, a_3, \ldots, a_n,\ldots\) is such that \(a_n= \dfrac1{n^2}-\dfrac1{(n-1)^2}\) for all integers

[Vincen]

The sequence \(a_1, a_2, a_3, \ldots, a_n,\ldots\) is such that \(a_n= \dfrac1{n^2}-\dfrac1{(n-1)^2}\) for all integers \(n\ge 2\) and \(a_1 = 1.\) Which of the following could be the sum of sequence if the number of terms in the sequence is a prime number?

A. \(\dfrac1{13}\)

B. \(\dfrac1{31}\)

C. \(\dfrac1{225}\)

D. \(\dfrac1{289}\)

E. \(\dfrac1{324}\)

Answer: D

Source: e-GMAT