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Use mathematical induction to prove that...

Use mathematical induction to prove that statement `1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/( 4) , AA n in N`

Answer

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Knowledge Check

  • If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

    A
    `1//2`
    B
    `1`
    C
    `3//2`
    D
    `2`

  • S_(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T_(n) = 1+ 2 + 3+ 4…...n

    A
    `S_(n) = T_(n)^(3)`
    B
    `S_(n) = T_(n^2) `
    C
    `S_(n) = T_(n)^(2)`
    D
    `S_(n) = T_(n)^(3)`

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    4^(3) + 8^(3) + 12^(3) + . . . upto n terms = 16n^(2) (n + 1)^(2)

    Using the principle of finite Mathematical Induction prove that 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2)) + "n terms" = (n(n+1)^(2)(n+2))/(12), AA n in N .

    Using Mathematical Induction, prove that statement for all n in N 1.2.3+2,3,4+……….+("upto n terms")=(n(n+1)(n+2)(n+3))/(4) .

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    Using the principle of finite Mathematical Induction prove that 1^2+(1^2+2^2)+(1^2+2^2+3^2)+.......n terms =(n(n+1)^2(n+2))/12,foralln in N

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