I want to prove that ∑x=1∞ln⁡xx2≤1

Shamar Padilla

Shamar Padilla

Answered

2022-01-22

I want to prove that
x=1lnxx21

Answer & Explanation

basgrwthej

basgrwthej

Expert

2022-01-23Added 13 answers

Note that
lnxx2dx=1+lnxx+C
Since lnxx2 is decreasing for x>2, we have
n=1ln24+ln39+n=4lnnn2
<ln24+ln39+3lnxx2dx
0.29535+0.69954
=0.99489

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