1.
Let Sn=cot12+cot18+cot118+cot132+S_n=\cot^{-1}2+\cot^{-1}8+\cot^{-1}18+\cot^{-1}32+\ldots to nthn^{\text{th}} term. Then limnSn\displaystyle\lim_{n\to\infty}S_n is