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sum(k=1)^20 k[1/k+1/(k+1)+1/(k+2)+.........

`sum_(k=1)^20 k[1/k+1/(k+1)+1/(k+2)+.........+1/20]`

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sum_(k=1)^ook(1-1/n)^(k-1) =?

Find sum_(k=1)^(n)(1)/(k(k+1)) .

Knowledge Check

  • sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

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

  • sum_(k=1)^(2n+1) (-1)^(k-1) k^2 =

    A
    `(n+1)(2n+1)`
    B
    `(n+1) (2n-1)`
    C
    `(n-1) (2n-1)`
    D
    `(n-1)(2n+1)`

    • Similar Questions

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    Find sum_(k=1)^(n)(1)/(k(k+1)) .

    sum_(k=1)^(2n+1)(-1)^(k-1)k^(2)=

    L = lim_ (n rarr oo) (1) / (n ^ (4)) [1.sum_ (k = 1) ^ (n) k + 2 * sum_ (k = 1) ^ (n-1) k + 3 * sum_ (k = 1) ^ (n-2) k + ......... + n.1]

    Find sum_(1)^(infty) 1/((k+1)(k+2))

    Value of L = lim_(n->oo) 1/n^4 [1 sum_(k=1)^n k + 2sum_(k=1)^(n-1) k + 3 sum_(k=1)^(n-2) k +.....+n.1] is

    Prove that sum_(k=1)^n 1/(k(k+1))=1−1/(n+1) .

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