Find \cot(\sum_{n=1}^{23} \cot^{-1} (1+\sum_{k=1}^n 2k)) I tried to simplify it but

William Montgomery

William Montgomery

Answered question

2022-01-25

Find cot(n=123cot1(1+k=1n2k))
I tried to simplify it but it became messy. How can I find n=123cot1(1+n+n2)?

Answer & Explanation

Damian Roberts

Damian Roberts

Beginner2022-01-26Added 14 answers

The hint.
Use
arctan(n+1)arctann=arot(n2+n+1)
and the telescopic summation.

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