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Integral that is continuous and looks like it converges to a geometric series

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Integral that is continuous and looks like it converges to a geometric series


Testing if a geometric series converges by taking limit to infinitySummation of arithmetic-geometric series of higher orderGeometric series with polynomial exponentHow to Recognize a Geometric SeriesShowing an integral equality with series over the integersDiscontinuity of a series of continuous functionsReasons why a Series ConvergesSum of infinite geometric series with two terms in summationUsing geometric series for computing IntegralsLimit of geometric series sum when $r = 1$













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enter image description here



I think the key word is continous. the RHS totally looks like a sum from a geometric series but I dont see a trick when I think there is one .










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    5












    $begingroup$


    enter image description here



    I think the key word is continous. the RHS totally looks like a sum from a geometric series but I dont see a trick when I think there is one .










    share|cite|improve this question









    $endgroup$















      5












      5








      5


      1



      $begingroup$


      enter image description here



      I think the key word is continous. the RHS totally looks like a sum from a geometric series but I dont see a trick when I think there is one .










      share|cite|improve this question









      $endgroup$




      enter image description here



      I think the key word is continous. the RHS totally looks like a sum from a geometric series but I dont see a trick when I think there is one .







      calculus integration multivariable-calculus improper-integrals






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      asked 5 hours ago









      Randin DRandin D

      1026




      1026






















          1 Answer
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          $begingroup$

          Hint: Let $g(x) = (x+1)^{2017}$. Let $h = f-g$. By the mean value theorem, there exists $a$ such that
          $$h(a) = int_0^1 h(x) , dx.$$






          share|cite|improve this answer









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          • $begingroup$
            aha ..do u have an email we can chat more about this problemo?
            $endgroup$
            – Randin D
            5 hours ago












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          1 Answer
          1






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          active

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          active

          oldest

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          4












          $begingroup$

          Hint: Let $g(x) = (x+1)^{2017}$. Let $h = f-g$. By the mean value theorem, there exists $a$ such that
          $$h(a) = int_0^1 h(x) , dx.$$






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            aha ..do u have an email we can chat more about this problemo?
            $endgroup$
            – Randin D
            5 hours ago
















          4












          $begingroup$

          Hint: Let $g(x) = (x+1)^{2017}$. Let $h = f-g$. By the mean value theorem, there exists $a$ such that
          $$h(a) = int_0^1 h(x) , dx.$$






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            aha ..do u have an email we can chat more about this problemo?
            $endgroup$
            – Randin D
            5 hours ago














          4












          4








          4





          $begingroup$

          Hint: Let $g(x) = (x+1)^{2017}$. Let $h = f-g$. By the mean value theorem, there exists $a$ such that
          $$h(a) = int_0^1 h(x) , dx.$$






          share|cite|improve this answer









          $endgroup$



          Hint: Let $g(x) = (x+1)^{2017}$. Let $h = f-g$. By the mean value theorem, there exists $a$ such that
          $$h(a) = int_0^1 h(x) , dx.$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 5 hours ago









          angryavianangryavian

          43k23482




          43k23482












          • $begingroup$
            aha ..do u have an email we can chat more about this problemo?
            $endgroup$
            – Randin D
            5 hours ago


















          • $begingroup$
            aha ..do u have an email we can chat more about this problemo?
            $endgroup$
            – Randin D
            5 hours ago
















          $begingroup$
          aha ..do u have an email we can chat more about this problemo?
          $endgroup$
          – Randin D
          5 hours ago




          $begingroup$
          aha ..do u have an email we can chat more about this problemo?
          $endgroup$
          – Randin D
          5 hours ago


















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