Thursday, 28 July 2016

real analysis - How to solve this limit limlimitsnrightarrowinfty,left(fracunvnright)2040?

Let (un)n and (vn)n be positive numerical sequences such that (1+2)n=un+vn2 with nN

How to determine the limit of
limn(unvn)2040



I start think to find such recessive sequence for u_n terms in order to separate them using induction but this leads to nothing . so as result is there any shortcut to attack this problem?

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