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

Find the sum series: `tan^-1 (1/3)+tan^-1 (1/7)+tan^-1(1/13)+…to oo`

A

`tan^(-1)((n)/(n+2))`

B

`tan^(-1)((2n-1)/(2n+1))`

C

`tan^(-1)((1)/(3n))`

D

`tan^(-1)((1)/(2n))`

Text Solution

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The correct Answer is:
A
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MCGROW HILL PUBLICATION-PROGRESSIONS-EXERCISES LEVEL-1 (Single Correct Answer Type Questions)
  1. Sum of first 'n' terms of the series 3/2+5/4+9/8+17/16+...

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  2. The sum of n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+.... is...

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  3. Find the sum series: tan^-1 (1/3)+tan^-1 (1/7)+tan^-1(1/13)+…to oo

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  4. FInd the sum of infinite terms of the series 1/(1.2.3)+1/(2.3.4)+1/(3...

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  5. If n!, 3n! and (n-1)! are in G.P then n!, 5n! and (n+1)! are in

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  6. If S(n)=81+54+36+24+.. upto n terms, then value of x=(S(n)-4S(n-1)+6S(...

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  7. The sum of first 'n' terms of the series 1^2+(1)(2)+3^2+(3)(4)+5^2+(5)...

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  8. If L = underset( n rarr oo)lim (1+3^(-1))(1+3^(-2))+(1+3^(-4))+(1+3^(-...

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  9. If a1,a2,a3,.......an, are 'n', distinct odd natural numbers, not divi...

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  10. Coefficient of x^(99) in the expansion of (x-1) (x-3)(x-5)..(x-1999) i...

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  11. Find the sum to n terms of the series 1 + (1 + 2) + (1 + 2 + 3) + .......

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  12. If x= overset(oo)underset(n =0)Sigma a^(n),y= overset(oo)underset(n=0)...

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  13. If the sum of an infinite decreasing G.P. is 3 and sum of the cubes of...

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  14. The sum of the series S= overset(n)underset(r=1)Sigma log ((a^(r+1))/(...

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  15. If the fifth term of a G.P. is 2, then write the product of its 9 t...

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  16. If s is the sum to infnity of a G.P, whose first term is a, then the s...

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  17. For a sequence lt a(n) gt, a(1) =5 and (a(r+1))/(a(r))=(1)/(2) AA r, t...

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  18. If the H.M.of two numbers is to their GM. is 12:13 then the numbers ar...

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  19. The H.M. between two numbers is 16/5, their A.M. is A and G.M. is G. I...

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  20. If a(r)=a+(r-1)d is rth term of an A.P., then a(n)^(2)-2a(n-1)^(2)+a(n...

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