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Let Sndenote the sum of the cubes of the...

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

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The correct Answer is:
A
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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))/(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

  • If the sum of first n natural numbers is one-fifth of the sum of their squares, then n is

    A
    5
    B
    6
    C
    7
    D
    8

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