SOLUTION: Prove that {{{6/(n+1) <= 6/(2n+1) +sqrt(sum(1/k^2, k=1,n))}}} for {{{n >= 1}}}.

Question 1062031: Prove that
for .
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Prove that

 for 

That will be true if and only if

 for 

Simplifying the expression on the left,

 for 

The proof is immediate because the left side decreases as
n gets larger and the right side increases as n gets larger,
so the inequality will always hold for .

Edwin

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