Question

For the following telescoping series, find a formula for the nth term of the sequence of partial sums ($S_n$). Then evaluate $\lim_{n \to \infty} S_n$ to obtain the value of the series or state that the series diverges. $\sum_{k=1}^{\infty} (8 \sec^{-1}(k+1) - 8 \sec^{-1}k)$ $S_n = $ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\lim_{n \to \infty} S_n = $ (Type an exact answer in terms of $\pi$.) B. The series diverges.

          For the following telescoping series, find a formula for the nth term of the sequence of partial sums ($S_n$). Then evaluate $\lim_{n \to \infty} S_n$ to obtain the value of the series or state that the series diverges.
$\sum_{k=1}^{\infty} (8 \sec^{-1}(k+1) - 8 \sec^{-1}k)$
$S_n = $
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\lim_{n \to \infty} S_n = $ (Type an exact answer in terms of $\pi$.)
B. The series diverges.

For the following telescoping series, find a formula for the nth term of the sequence of partial sums (Sn). Then evaluate limn →∞ Sn to obtain the value of the series or state that the series diverges.
∑k=1^∞ (8 sec^-1(k+1) - 8 sec^-1k)
Sn =
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. limn →∞ Sn = (Type an exact answer in terms of π.)
B. The series diverges.

Added by Joseph U.

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