Let Sn = Σ n/n^2+kn+k^2; k=0, n & Tn = Σ n/n^2+kn+k^2; k=0, n-1 for n= 1, 2, 3 then

Question

Let \(S_n = \sum\limits_{k =0}^n \frac{n}{n^2 + kn + k^2}\) & \(T_n = \sum\limits_{k =0}^{n-1} \frac{n}{n^2 + kn + k^2}\) for n = 1, 2, 3 then

(a) \(S_n < \frac \pi{3\sqrt3}\)

(b) \(S_n > \frac \pi{3\sqrt3}\)

(c) \(T_n < \frac \pi{3\sqrt3}\)

(d) \(T_n > \frac \pi{3\sqrt3}\)

Answer 1

Correct options are (a) & (d).