Friday, 8 November 2019

sequences and series - ak=limlimitsntoinftysumlimitsm=knm=1frac1nefracm22n2

ak=limnm=knm=11nem22n2



Find limkak



I tried using integral test and it resulted to nothing . ultimately I took the help of Central limit Theorem , even though it is completely wrong .



ak=limnm=knm=11(2π)n2πe(m0)22n2




ak=limn2πm=knm=11n2πe(m0)22n2,where m is N(0,n2)



ak=limn2πP(1mkn)=limn2πP(1nmnknn)



ak=2πlimn(Φ(k)Φ(1n))=2π(Φ(k)12)



limkak=π2



Any helpful insights?

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