We have, cotn=1∑19(cot−1(1+p=1∑n2p))
=cotn=1∑19tan−1(1+n(n+1)1)
=cotn=1∑19tan−1(1+n(n+1)n+1−n)
=cotn=1∑19(tan−1(n+1)−tan−1(n))
=cot(tan−120−tan−11)
=tan(tan−120−tan−11)1
=1+(20).120−11=1921
The value of cot(n=1∑19cot−1(1+p=1∑n2p)) is:
Held on 10 Jan 2019 · Verified 6 Jul 2026.
1921
2119
2223
2322
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