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If S1,S2,S3are the sum of first n natur...

If `S_1,S_2,S_3`are the sum of first n natural numbers, their squares and their cubes, respectively, show that `9S_2^2=S_3(1+8S_1)`.

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Knowledge Check

  • If S_(1), S_(2) and S_(3) are the sums of first n natureal numbers, their squares and their cubes respectively, then (S_(1)^(4)S_(2)^(2)-S_(2)^(2)S_(3)^(2))/(S_(1)^(2) +S_(2)^(2))=

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    A
    A.P.
    B
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    C
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    none

  • If S_(1), S_(2), S_(3) be the sum of n, 2n, 2n terms respectively of an A.P., then

    A
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    B
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    C
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    D
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    If S_(1),S_(2),S_(3) are the sums of first n natural numbers,their squares and their cubes respectively then S_(3)(1+8S_(1))=

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