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Let S (K) = sum (r=1) ^(k) tan ^(-1) (( ...

`Let S _(K) = sum _(r=1) ^(k) tan ^(-1) (( 6 ^r)/( 2 ^( 2 r + 1) + 3 ^( 2r +1))) .` Then `lim _( k to oo) S _(k)` is equal to :

A

`pi/2`

B

`tan ^(-1) (3)`

C

`tan ^(-1) ((3)/(2))`

D

`cot ^(-1) ((3)/(2))`

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Knowledge Check

  • Let S_(n) = sum_(k=1)^(4n) (-1) (k(k-1))/(2), k^(2) . Then S_n can take values

    A
    `1056`
    B
    `1088`
    C
    `1120`
    D
    `1332`

  • If sum_(r = 1)^(oo) "tan"^(-1)(1)/(2r^(2))=t , then tan t is equal to

    A
    0
    B
    1
    C
    `sqrt(3)`
    D
    `1//sqrt(3)`

  • If A = lim_(n rarr oo) sum_(r = 1)^(n) tan^(-1) ((1)/(2r^(2))) , then A is equal to

    A
    `(pi)/(4)`
    B
    1
    C
    `(pi)/(3)`
    D
    `lt 1`

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