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cot-(1)/(4)+cot^(-1)8+ct^(-1)18...

cot-(1)/(4)+cot^(-1)8+ct^(-1)18

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Let S_(n)=cot^(-1)2 +cot^(-1)8 +cot^(-1)18 +cot^(-1)32+…. to n^(th) term. Then lim_(n to oo)S_(n) is

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Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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The sum of the series cot^(-1)2+cot^(-1)8+cot^(-1)18+cot^(-1)32.........

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Prove that: tan^(-1)(1)/(7)+tan^(-1)(1)/(13)=tan^(-1)(2)/(9)tan^(-1)+tan^(-1)(1)/(5)+tan^(-1)(1)/(8)=(pi)/(4)tan^(-1)(3)/(4)+tan^(-1)(3)/(5)-tan^(-1)(8)/(19)=(pi)/(4)tan^(-1)(1)/(5)+tan^(-1)(1)/(7)+tan^(-1)(1)/(3)+tan^(-1)(1)/(8)=(pi)/(4)cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)(1)/(13)