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**fardeen_gen** If $\displaystyle x_1,x_2,x_3,\mbox{...}$ are in arithmetic progression with common difference $\displaystyle d$, show that:

$\displaystyle \mbox{arccot}\left(\frac{1 + x_{1}x_{2}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{2}x_{3}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{3}x_{4}}{d}\right) + \mbox{...} $ $\displaystyle +\ \mbox{arccot}\left(\frac{1 + x_{n}x_{n + 1}}{d}\right) = \mbox{arccot}\left(\frac{1 + x_{1}x_{n + 1}}{d}\right)$, where $\displaystyle x_1 > 0$ and $\displaystyle d > 0$