Proof of generalization of a particular limit converging to e <mrow class="MJX-TeXAto

Finley Mckinney

Finley Mckinney

Answered question

2022-06-15

Proof of generalization of a particular limit converging to e 1 ( p 1 ) 2
I was reading a very old and long article on logarithms in a library it has pages turned yellow and had one pages titled - Tricky problems I managed to solve 5 out of the 6 but I couldn't do this 6th one . Prove that for all p N
lim n ( 1 1 p × 2 2 p × 3 3 p × n n p ) n 1 p + 1 = e 1 ( p 1 ) 2
I tried to manupilate this with the properties of logarithms but failed.

Answer & Explanation

benedictazk

benedictazk

Beginner2022-06-16Added 22 answers

It seems to be wrong. The logarithm of the lhs is
HurwitzZeta ( 1 , 0 ) ( p , n + 1 ) log ( n ) p + 1 ζ ( p )
which goes to infinity with n

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