Thursday, May 26, 2016

real analysis - sumlimitsinftyn=1n(frac23)n Evalute Sum












How can you compute the limit of
n=1n(2/3)n



Evidently it is equal to 6 by wolfram alpha but how could you compute such a sum analytically?


Answer



n=1n(2/3)n=m=1n=m(2/3)n=m=1(2/3)m12/3=2/3(12/3)2=6.


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