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Math Help - summation of series

  1. #1
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    summation of series

    can you tell me how to calculate the sum of series : 1/(n*(n+1)*(n+2)) ?
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  2. #2
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    Re: summation of series

    Quote Originally Posted by nitin1 View Post
    can you tell me how to calculate the sum of series : 1/(n*(n+1)*(n+2)) ?

    Is this the question, \sum\limits_{n = 1}^\infty  {\frac{1}{{n\left( {n + 1} \right)\left( {n + 1} \right)}}}~?
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  3. #3
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    Re: summation of series

    no.. not till infinity... it's upto only n.. like from 1 to 3 or 1 to 4 or say 1 to n... and the question is summation of 1/(n*(n+1)*(n+2)) .. this is nth term of the series...
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  4. #4
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    Re: summation of series

    Quote Originally Posted by nitin1 View Post
    no.. not till infinity... it's upto only n.. like from 1 to 3 or 1 to 4 or say 1 to n... and the question is summation of 1/(n*(n+1)*(n+2)) .. this is nth term of the series...

    Well note that \frac{1}{n(n+1)(n+2)}=\frac{1}{2n}-\frac{1}{(n+1)}+\frac{1}{2(n+2)}.

    Write out several terms to see if some pattern is there.
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  5. #5
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    Re: summation of series

    i have got this result from someone...

    S(n)= 1/4 - 1/(2*(n+2)*(n+1))...

    it is correct even! can you tell me the steps taken so as to achieve this result ? please! thanks.
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