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Question

Evaluate the infinite series: ∑m=0∞(tan⁡−1(m+3)−tan⁡−1(m+1)) \displaystyle \sum_{m=0}^{\infty} \left( \$$tan^{-1}(m+3$$) - \$$tan^{-1}(m+1$$) \right) .

Accepted Answer

3π4−tan⁡−12\frac{3\pi}{4}-\$$tan^{-1}2$$

Answer

π2−tan⁡−12\frac{\pi}{2}-\$$tan^{-1}2$$

Answer

π2\frac{\pi}{2}

Answer

3π4−tan⁡−13\frac{3\pi}{4}-\$$tan^{-1}3$$

Evaluate the infinite series: ∑m=0∞(tan−1(m+3)−tan−1(m+1)) \(\displaystyle\) \(\sum\)_{m=0}^{\(\infty\)} \(\left\)( \(\tan\)^{-1}(m+3) - \(\tan\)^{-1}(m+1) \(\right\)) .

Evaluate the infinite series: $\sum_{m = 0}^{\infty} (\tan^{- 1} (m + 3) - \tan^{- 1} (m + 1))$ .