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Let Sn denote the sum of the cubes of th...

Let `S_n` denote the sum of the cubes of the first `n` natural numbers and `s_n` denote the sum of the first `n` natural numbers. Then `sum_(r=1)^n S_r/s_r` is equal to

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let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers , then sum_(r=1)^(n)(S_(r))/(s_(r)) equals to

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Knowledge Check

  • Let S_n denote the sum of the cubes of the first n natural numbers and s_n denote the sum of the first n natural numbers. Then, sum_(r=1)^n(S_r)/(8_r) is equal to

    A
    `(n(n+1)(n+2))/6`
    B
    `(n(n+1))/2`
    C
    `(n^2+3n+2)/2`
    D
    None of these

  • Let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers. Then sum_(r=1)^(n)(S_(r))/( S_(r )) equals :

    A
    `( n (n+1)(n+2))/( 6)`
    B
    `(n(n+1))/( 2)`
    C
    `(n^(2) + 3n+2)/( 2)`
    D
    None of these

  • let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers , then sum_(r=1)^(n)(S_(r))/(s_(r)) equals to

    A
    `(n(n+1)(n+2))/(6)`
    B
    `(n(n+1))/(2)`
    C
    `(n^(2)+3n+2)/(2)`
    D
    None of these

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    Let S_(n) denote the sum of the cubes of the first n natural numbers and S'_(n) denote the sum of the first n natural numbers, then underset(r=1)overset(n)Sigma ((S_(r))/(S'_(r))) equals to

    Let S_n denote the sum of the first n terms of an AP S_(2n)=3S_n Then the ratio S_(3n)/S_n is equal to

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