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 \(a_1 = 1.\) Is the sum of this sequence greater than \(0.005?\)

(1) The number of terms in the sequence is greater than \(12.\)

(2) The number of terms in the sequence is lesser than \(14.\)

Answer: B

Source: e-GMAT