S=tan−131+tan−171+tan−1131+…… up to10 terms.
S=tan−1(1+1.22−1)+tan−1(1+2.33−2)+tan−1(1+3.44−3)+……+tan−1(1+11.1011−10)
⇒S=(tan−12−tan−11)+(tan−13−tan−12)+……+(tan−111−tan−110)
⇒S=tan−111−tan−11
⇒S=tan−1(1+11⋅111−1)=tan−1(1210)
∴tan(S)=65
If S is the sum of the first 10 terms of the series, tan−1(31)+tan−1(71)+tan−1(131)+tan−1(211)+…… then tan(S) is equal to :
Held on 5 Sept 2020 · Verified 6 Jul 2026.
65
115
−65
1110
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