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Math Help - SUm

  1. #1
    Senior Member
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    SUm

    Find the first three terms and the nth term of the series with the sum to n terms , S_n , given by :

    (1) S_n=4n-\frac{1}{n}

    I know the first three terms . The answer given by the book for the nth term is :

     4+\frac{1}{n(n-1)},n>1

    My question is if that's the answer , why can't i get the first term which is 3 when i substitute n=1 into the formula .

    And if it says n is greater than 1 , then there is no way to find the first term.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thereddevils View Post
    Find the first three terms and the nth term of the series with the sum to n terms , S_n , given by :

    (1) S_n=4n-\frac{1}{n}

    I know the first three terms . The answer given by the book for the nth term is :

     4+\frac{1}{n(n-1)},n>1

    My question is if that's the answer , why can't i get the first term which is 3 when i substitute n=1 into the formula .

    And if it says n is greater than 1 , then there is no way to find the first term.
    The form for the general term a_n only applies to n>1 (you need S_{n-1} to get this from the sum to n terms so only applies when S_{n-1} is given by the formula. But S_0=0 so the first term:

    a_1=S_1

    CB
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