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Find the sum of the series :(tan^- 1)1/3...

Find the sum of the series :`(tan^- 1)1/3+(tan^- 1)2/9+....+(tan^- 1)(2^(n-1))/(1+2^(2n-1))+...... oo`

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The correct Answer is:
`(pi)/4`
NA
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RESONANCE-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
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  2. If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cosec^(-1)z,...

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  3. Consider f(x)=tan^(-1)(2/x),g(x)=sin^(-1)(2/(sqrt(4+x^(2)))) and h(x)=...

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  4. Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x...

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  5. Prove each of the following relation: cos^(-1)x=sec^(-1)1/x=pi-sin^(...

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  6. Express in terms of : "tan"^(-1)(2x)/(1-x^(2) to tan^(-1)x for xgt1

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  7. Express in terms of : sin^(-1)(2xsqrt(1-x^(2))) to sin^(-1)x for 1gexg...

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  9. Simplity tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)(1-y^(2))/(1+y^(2)...

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  10. Solve for x : cos(2sin^(-1)x)=1/3

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  11. Solve for x : cot^(-1)x+tan^(-1)3=(pi)/2

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  12. Solve : tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=pi/4

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  13. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

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  14. Prove that sin^(- 1)(8/17)+sin^(- 1)(3/5)=sin^(- 1)(77/85)

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  15. Prove that : "tan"^(-1)3/4+"sin"^(-1)5/13="cos"^(-1)33/65

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  16. Prove: sin^(-1)(1/sqrt5)+cot^(-1)3=pi/4

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  17. Prove that ta n^-1 1/3 + ta n ^-1 1/5 + ta n ^-1 1/7 + ta n ^-1 1/8 =...

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  18. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

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  19. Find the sum of the series :(tan^- 1)1/3+(tan^- 1)2/9+....+(tan^- 1)(2...

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  20. The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)...

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