My Math Forum Calculate series (Geometric or harmonic)

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December 4th, 2016, 06:30 AM   #1
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Calculate series (Geometric or harmonic)

Hello,
How can solve this?
I think The numerator is harmonic.
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 December 4th, 2016, 10:27 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Is the upper bound supposed to be $\displaystyle \log_2(n)$? If so, then the summation only makes sense for n a power of 2. And is the logarithm in the denominator of the summand to base 2? For example, if n= 2, then $\displaystyle \log_2(n)= 1$ so the summation is from i= 0 to 1: $\displaystyle \frac{\frac{2}{1}}{\log_2(\frac{2}{1})}+ \frac{\frac{2}{2}}{\log_2(\frac{2}{2})}= \frac{2}{1}+ \frac{2}{0}$ Hmm! since $\displaystyle \log(1)= 0$, that will always have a 0 in the denominator of a fraction so the summation does not exist! Last edited by skipjack; December 5th, 2016 at 05:07 AM.
 December 4th, 2016, 11:28 AM #3 Newbie   Joined: Jun 2016 From: Poland Posts: 14 Thanks: 2 So let us change the left border of sum $\displaystyle i=2$ Last edited by skipjack; December 5th, 2016 at 05:05 AM.

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