Question 1062031
<pre>
Prove that

{{{6/(n+1) <= 6/(2n+1) +sqrt(sum(1/k^2, k=1,n))}}} for {{{n >= 1}}}

That will be true if and only if

{{{6/(n+1) - 6/(2n+1)  <= sqrt(sum(1/k^2, k=1,n))}}} for {{{n >= 1}}}

Simplifying the expression on the left,

{{{(6n)/((n+1)(2n+1))  <= sqrt(sum(1/k^2, k=1,n))}}} for {{{n >= 1}}}

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 {{{n >= 1}}}.

Edwin</pre>