Thursday, June 9, 2016

real analysis - Why this :sumlimitsinftyn=0(0)=0?



I'm confused how :n=00=0 but after evaluation we w'd get 0. which it's indeterminate case and wolfram alpha show here that is a convergent series which it's equal's 0, i'm only sure that is 0 for it partial sum .



My question here is : Is there somone who show me how do I convince my self by :n=00=0 ?



Thank you for any help


Answer




By definition, one has
n=0an=limNNn=0an

giving
n=00=limNNn=00=limN0=0.


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