Question 578016
Your multiplication middle dots came out as decimal points, and that puzzled us.
{{{(1&1/2)^2=1*2+1/4}}}
{{{(2&1/2)^2=2*3+1/4}}}
{{{(3&1/2)^2=3*4+1/4}}}
{{{(n+1/2)^2=n*(n+1)+1/4}}}
{{{(n+1/2)^2=n^2+2*(1/2)*n+(1/2)^2=n^2+n+1/4=n(n+1)+1/4}}}