Tuesday, February 5, 2019

sequences and series - Find the limit limlimitsntoinftyfrac2n2sumlimitsinftyk=n+12k2




Find the limit of the following-lim




My work:



We can see that the denominator is in geometric series, whose sum is 1. So taking the limit we get \infty? Am I right? But I think there is a problem in this reasoning as the powers are not starting from 0 or 1. Can we really consider a geometric series? Any help would be great. Thanks



Answer



Hint : Multiply denominator and numerator with 2^{n^2}


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