upper bound of p-series

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I saw the following relationship used in a couple of papers: $sum_t=2^infty frac1t^alphale frac1alpha-1$ for $alpha>1$. Can anyone explain how this relationship is obtained? Thanks.




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    I saw the following relationship used in a couple of papers: $sum_t=2^infty frac1t^alphale frac1alpha-1$ for $alpha>1$. Can anyone explain how this relationship is obtained? Thanks.




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      I saw the following relationship used in a couple of papers: $sum_t=2^infty frac1t^alphale frac1alpha-1$ for $alpha>1$. Can anyone explain how this relationship is obtained? Thanks.




      sequences-and-series




      share|cite|improve this question











      I saw the following relationship used in a couple of papers: $sum_t=2^infty frac1t^alphale frac1alpha-1$ for $alpha>1$. Can anyone explain how this relationship is obtained? Thanks.





      sequences-and-series





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      asked Jul 20 at 22:17









      Justin

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          If you're familiar with the integral test, you have probably seen inequalities like this:
          $$
          sum_t=2^infty t^-alphaleint_1^infty t^-alpha, alpha>1
          $$
          Does the argument make sense from here?






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          • Thanks. Yes, it works.
            – Justin
            Jul 24 at 14:26










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          up vote
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          If you're familiar with the integral test, you have probably seen inequalities like this:
          $$
          sum_t=2^infty t^-alphaleint_1^infty t^-alpha, alpha>1
          $$
          Does the argument make sense from here?






          share|cite|improve this answer























          • Thanks. Yes, it works.
            – Justin
            Jul 24 at 14:26














          up vote
          0
          down vote













          If you're familiar with the integral test, you have probably seen inequalities like this:
          $$
          sum_t=2^infty t^-alphaleint_1^infty t^-alpha, alpha>1
          $$
          Does the argument make sense from here?






          share|cite|improve this answer























          • Thanks. Yes, it works.
            – Justin
            Jul 24 at 14:26












          up vote
          0
          down vote










          up vote
          0
          down vote









          If you're familiar with the integral test, you have probably seen inequalities like this:
          $$
          sum_t=2^infty t^-alphaleint_1^infty t^-alpha, alpha>1
          $$
          Does the argument make sense from here?






          share|cite|improve this answer















          If you're familiar with the integral test, you have probably seen inequalities like this:
          $$
          sum_t=2^infty t^-alphaleint_1^infty t^-alpha, alpha>1
          $$
          Does the argument make sense from here?







          share|cite|improve this answer















          share|cite|improve this answer



          share|cite|improve this answer








          edited Jul 20 at 23:10


























          answered Jul 20 at 22:43









          Kajelad

          1,893619




          1,893619











          • Thanks. Yes, it works.
            – Justin
            Jul 24 at 14:26
















          • Thanks. Yes, it works.
            – Justin
            Jul 24 at 14:26















          Thanks. Yes, it works.
          – Justin
          Jul 24 at 14:26




          Thanks. Yes, it works.
          – Justin
          Jul 24 at 14:26












           

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