Progressions - Is it G.P. or H.P.?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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I came across the following example yesterday and could not figure it out. Any help is really appreciated.



Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....







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  • Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
    – Anik Bhowmick
    Aug 14 at 9:15














up vote
1
down vote

favorite
1












I came across the following example yesterday and could not figure it out. Any help is really appreciated.



Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....







share|cite|improve this question




















  • Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
    – Anik Bhowmick
    Aug 14 at 9:15












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





I came across the following example yesterday and could not figure it out. Any help is really appreciated.



Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....







share|cite|improve this question












I came across the following example yesterday and could not figure it out. Any help is really appreciated.



Find the sum of the following progression from 1st to 1000th term
3, 5/3, 7/5, 9/7, 11/9, ....









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 14 at 9:11









Prateek West

61




61











  • Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
    – Anik Bhowmick
    Aug 14 at 9:15
















  • Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
    – Anik Bhowmick
    Aug 14 at 9:15















Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
– Anik Bhowmick
Aug 14 at 9:15




Welcome to Mathematics Stack Exchange !! Here we can help you in any kind of mathematical problems, but you have to show what you have tried. Here, the given series is neither in G.P nor in H.P. They are just in form of $(2k+1)/(2k-1)$.
– Anik Bhowmick
Aug 14 at 9:15










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I have only bad news



$$frac 2k+12k-1=1+frac 22k-1$$



So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:



$$sum_n=1 ^N frac 1 n $$



Much less this:



$$sum_n=1 ^N frac12 n -1$$






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote













    I have only bad news



    $$frac 2k+12k-1=1+frac 22k-1$$



    So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:



    $$sum_n=1 ^N frac 1 n $$



    Much less this:



    $$sum_n=1 ^N frac12 n -1$$






    share|cite|improve this answer
























      up vote
      1
      down vote













      I have only bad news



      $$frac 2k+12k-1=1+frac 22k-1$$



      So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:



      $$sum_n=1 ^N frac 1 n $$



      Much less this:



      $$sum_n=1 ^N frac12 n -1$$






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        I have only bad news



        $$frac 2k+12k-1=1+frac 22k-1$$



        So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:



        $$sum_n=1 ^N frac 1 n $$



        Much less this:



        $$sum_n=1 ^N frac12 n -1$$






        share|cite|improve this answer












        I have only bad news



        $$frac 2k+12k-1=1+frac 22k-1$$



        So your sum depends on the harmonic sum of the odds, which depends on a finite sum of the harmonic series itself. No one has a clean closed form formula for this:



        $$sum_n=1 ^N frac 1 n $$



        Much less this:



        $$sum_n=1 ^N frac12 n -1$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 14 at 9:48









        AmateurMathPirate

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