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Value of underset(n rarr infty )(Lim) su...

Value of `underset(n rarr infty )(Lim) sum_(r = 1)^(n) Tan^(-1) ((1)/(2r^(2))) ` is

A

`pi//2`

B

`pi//4`

C

1

D

none of these

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. Between 1 and 31 are inserted m arithmetic means, so that the ratio of...

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  2. If a(1), a(2) ……… a(n) are in A.P with common difference d ne 0, then ...

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  3. Value of underset(n rarr infty )(Lim) sum(r = 1)^(n) Tan^(-1) ((1)/(2r...

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  4. Given that n A.M.s are inserted between two sets of numbers a , 2b and...

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  5. If pth, qth, rth terms of an A.P are a,b,c then a(q - r ) + b(r - p ) ...

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  6. If mth terms of an A.P . Is n and nth term is m, then (m + n)th term i...

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  7. If the mth term of an A.P is n and nth term is m , then pth term =

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  8. If 100 times the 100^(th) term of an A.P with non zero common differen...

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  9. If the sum of m terms of an A.P, is equal to the sum of n terms of the...

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  10. If a(1), a(2) …… a(n) are in A.P then (sqrt(a(1)) + sqrt(a(n)))/( sqrt...

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  11. If the ratio of sum of n terms in two A.P' s is 2n : n + 1, then the ...

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  12. The sum of n terms in two A.P's are in the ratio 3n + 1 : n + 4 , then...

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  13. If S(n) danotes the sum of n terms of n terms of an A.P. then S(n + 3)...

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  14. The first term of an A.P of consecutive integers is p^(2) + 1 . The su...

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  15. The numbers 3^(2 sin 20 -1 ) , 14, 3^(4 - 2 sin 20) form first three ...

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  16. Arithmetic mean of 1/2 & 1/3 is

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  17. One of the four A,M's between 3, 23 is

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  18. Sum of 4 Arithmetic means between 3 and 23 is

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  19. Sum of 14 A.M's between 5 and 8 is

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  20. If n arithmetic means are inserted between 2 and 38 , then the sum of ...

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