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Using the principle of finite Mathematical Induction prove that 1.2.3+2.3.4+3.4.5.+………… upto n terms = n(n+1)(n+2)(n+3))/4,for all n in N

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Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .

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

Knowledge Check

  • 2+ 3.2 + 4.2^(2) + …... upto n terms =

    A
    `(n+1) 2^(n-1)`
    B
    `n2^(n+1)`
    C
    `n2^(n)`
    D
    `(n+1)2^(n)`

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    Using the principle of finite Mathematical Induction prove the following: (vi) 2+3.2+4.2^(2)+………."upto n terms" = n.2^(n) .

    2 . 3 + 3.4 + 4.5 + ... upto n terms

    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 the principle of finite Mathematical Induction prove the following: (iii) 1/(1.4) + 1/4.7 + 1/7.10 + ……… + "n terms" = n/(3n+1) .

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