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Using the principle of finite Mathematic...

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

Using the principle of finite Mathematical Induction prove the following: (iv) a+ar+ar^(2)+……..+"n terms" = (a(r^(n)-1))/(r-1) , r != 1 .

Knowledge Check

  • 1+ 3+ 7 + 15… n terms =

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

  • 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

    A
    `2n^(3) + 2n^(2)`
    B
    `(1)/( 6) (n^(3) + 3n^(2) + 1)`
    C
    `2n^(3) + 2n`
    D
    `2n^(3) - 2n^(2)`

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    Using the principle of finite Mathematical Induction prove the following: (v) 3.5^(2n+1)+2^(3n+1) is divisible by 17, AA n in N .

    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 1.2.3+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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