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cot^(-1) (2^2+1/2)+cot^(-1) (2^3+1/2^2)+...

`cot^(-1) (2^2+1/2)+cot^(-1) (2^3+1/2^2)+cot^(-1)(2^4+1/2^3)+…… oo`

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The correct Answer is:
A, B
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Explore conceptually related problems

The sum to infinite terms of the series cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+

If the sum of first 16 terms of the series s=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+ up to terms is cot^(-1)((1+2^(n))/(2(2^(16)-1))), then find the value of n.

Knowledge Check

  • Find the sum to n terms of the series S_(n)=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+..... upto n terms ?

    A
    `tan^(-1)(2^(n))-tan^(-1)(2)`
    B
    `tan^(-1)(2^(n+1))-tan^(-1)(2)`
    C
    `tan^(-1)(2^(2n))-tan^(-1)(2)`
    D
    None of these

  • The value of the expression cot^(-1) (1/2) + cot^(-1) (9/2) + cot^(-1) (25/2) + cot^(-1) (49/2) upto + .......n terms is

    A
    `tan^(-1) 2n`
    B
    `tan^(-1) (2n - 1)`
    C
    `tan^(-1)n`
    D
    `tan^(-1) 2n - tan^(-1) 1`

  • Sum of infinite terms of the series cot^(-1) ( 1^(2) + 3/4) + cot^(-1) ( 2^(2) + 3/4) + cot^(-1) ( 3^(2) + 3/4) + ... is

    A
    ` pi//4`
    B
    `tan^(-1)2`
    C
    `tan^(-1) 3`
    D
    `tan^(-1) 4`

    • Similar Questions

    Explore conceptually related problems

    If A = 1/1 cot ^(-1) (1/1) + 1/2 cot^(-1) (1/2) + 1/3 cot ^(-1) ( 1/3) " and " B = 1 cot^(-1) ( 1) + 2 cot^(-1) (2) + 3 cot^(-1) (3) " then " |B - A| " is equal to " (api)/b + c/d cot ^(-1) (3) where a,b,c,d in N are in their lowest form , find ( b -a - c - d)

    (cot^(-1)x^(2))^(3)

    cot^(-1)(2cdot1^2)+cot^(-1)(2cdot2^2) +cot^(-1)(2cdot3^2)+... upto infty is equal to

    cot^(-1)(2*1^(2))+cot^(-1)(2*2^(2))+cot^(-1)(2*3^(2))+... "upto "infty is equal to

    cot^(-1)(-1/2)+cot^(-1)(-1/3) is equal to

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