Sum or upped bound of geometricoharmonic seriesby aamir.ahmed Tags: geometric series, harmonic series, infinite series 

#1
Jun2010, 05:15 PM

P: 2

Hi,
I need help to determine the upper bound of this infinite series. [tex]\sum_{k=p+1}^{\infty} \frac{1}{k} a^k \ \ \ \ ; a \leq 1[/tex] The paper I am reading reports the upper bound to be, [tex]\sum_{k=p+1}^{\infty} \frac{1}{k} a^k \leq \frac{1}{p+1}\sum_{k=p+1}^{\infty} a^k = \frac{1}{p+1} \cdot \frac{a^{p+1}}{1a}[/tex] I totally cannot understand how could he factor 1/k coefficient out of the summation and replace it with 1/(p+1). Please point me in the right direction. 



#2
Jun2010, 09:33 PM

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