Question

prove that 2[1+(logn)²/2!+(logn)⁴/4!+(logn)⁶/6!+...)=n+1/n​

Answer 1

Answer:

Check the conditions fit for the Condensation Test :

an:=1nlogn⟹2na2n=2n2nlog2n=1log21n

and since the series of the rightmost sequence is just a multiple of the harmonic series and thus diverges, also our series diverges.