1.
Let Sn=cot⁡−12+cot⁡−18+cot⁡−118+cot⁡−132+…S_n=\cot^{-1}2+\cot^{-1}8+\cot^{-1}18+\cot^{-1}32+\ldots to nthn^{\text{th}} term. Then lim⁡n→∞Sn\displaystyle\lim_{n\to\infty}S_n is