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The sum of the infinite series 5/(3^2xx7...

The sum of the infinite series `5/(3^2xx7^2)+9/(7^2xx11^2)+13/(11^2xx15^2)+....` is

Answer

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Sum of series 5/(3^2 7^2)+9/(7^2 11^2)+13/(11^2 15^2)+....oo is

Finds the sum of first n terms of the series 3/(1^2xx2^2)+5/(2^2xx3^2)+7/(3^2xx4^2)+...... and hence deduce the sum of infinity.

Knowledge Check

  • The sum of the infinite terms of the series 5/(3^2. 7^2)+9/(7^2. 11^2)+13/(11^2. 15^2)..... is

    A
    1/12
    B
    1/36
    C
    1/54
    D
    1/72

  • The sum of the series 1/(3xx7)+1/(7xx11)+1/(11xx15)+... is

    A
    `1/3`
    B
    `1/6`
    C
    `1/9`
    D
    `1/12`

  • The sum of the series (1)/(3 xx 7) + (1)/(7 xx 11) + (1)/(11 xx 15)+… to oo is

    A
    `1//3`
    B
    `1//6`
    C
    `1//9`
    D
    `1//12`

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    The sum of the series (1)/(3xx7)+(1)/(7xx11)+(1)/(11xx15)+.... is

    Find the sum of the infinite series 1.3/2+ 3.5/2^2+ 5.7/2^3+ 7.9/2^4+.......oo

    Find the sum of the infinite series (1.3)/(2)+(3.5)/(2^(2))+(5.7)/(2^(3))+(7.9)/(2^(4))+......oo

    Find the sum to n terms of the series . 3 xx 1^(2) + 5 xx 2^(2) + 7 xx 3^(2) + . . . . . .

    Find the sum to n terms of the series 3xx1^2+5xx2^2+7xx3^2+ ………

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