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Math Help - need help on sequences topic

  1. #1
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    need help on sequences topic

    Find and simplify an expression for the sum of the natural numbers from (n + 1) to 2n inclusive.
    i tried to solve it but couldnt i came to 0.5*(3n+1)(n-1) ...this is the answer according to my book (3/2)n^2 + n/2. could someone hint me towards getting this answer
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    Re: need help on sequences topic

    Quote Originally Posted by abdulrehmanshah View Post
    Find and simplify an expression for the sum of the natural numbers from (n + 1) to 2n inclusive. according to my book (3/2)n^2 + n/2.

    \sum\limits_{k = n + 1}^{2n} k  = \sum\limits_{k = 1}^{2n} k  - \sum\limits_{k = 1}^n k
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    Re: need help on sequences topic

    edit: pipped at the post!
    Last edited by MarkFL; December 25th 2012 at 03:30 AM.
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    Re: need help on sequences topic

    It is an AP with the first term = ( n+1), common difference 1 and last term = 2n
    Also from n+1 to 2n we have n terms.
    Using expression for sum of n terms of an AP we get S = n/2 [ 2a + ( n-1) d )
    Thus we have (n+1) + ( n+2) + (n+3) + ..... + 2n = n/2 [ 2(n+1) + ( n-1) x 1 ] = n/2 [ 2n + 2 + n - 1 ] = n/2[ 3n + 1 ] = (3/2 ) n^2 + (n/2)
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    Re: need help on sequences topic

    Quote Originally Posted by ibdutt View Post
    It is an AP with the first term = ( n+1), common difference 1 and last term = 2n
    Also from n+1 to 2n we have n terms.
    Using expression for sum of n terms of an AP we get S = n/2 [ 2a + ( n-1) d )

    In order to do these problems you should know the so-called Gauss Sum:
    \sum\limits_{k = 1}^M k  = \frac{{M\left( {M + 1} \right)}}{2}.

    So according to that we get \frac{{2n(2n + 1)}}{2} - \frac{{n(n + 1)}}{2}.
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