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Math Help - Is is possible to use Arithmetic progression in this case?

  1. #1
    Junior Member
    Joined
    Oct 2009
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    Is is possible to use Arithmetic progression in this case?

    n
    \sum  e^\frac{i}{n}(\frac{1}{n})
    i = 1

    \frac{1}{n}[ e^\frac{1}{n} + e^\frac{2}{n} + e^\frac{3}{n} +.....+ e^\frac{n}{n} ]

    Did i compute wrongly ? I find it a bit weird. I can't proceed further on combining the bracket terms.

    Thanks.
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  2. #2
    Member
    Joined
    May 2009
    From
    New Delhi
    Posts
    153
    Quote Originally Posted by xcluded View Post
    n
    \sum  e^\frac{i}{n}(\frac{1}{n})
    i = 1

    \frac{1}{n}[ e^\frac{1}{n} + e^\frac{2}{n} + e^\frac{3}{n} +.....+ e^\frac{n}{n} ]

    Did i compute wrongly ? I find it a bit weird. I can't proceed further on combining the bracket terms.

    Thanks.
    [ e^\frac{1}{n} + e^\frac{2}{n} + e^\frac{3}{n} +.....+ e^\frac{n}{n} ]
    it is in geometric progression with common ratio
    = e^\frac{1}{n}
    use sum of infinite G.P. terms formula
    = \frac{a}{1-r}
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