$\begin{eqnarray*}{(0+1)^2\over 2}&=&{0^2+2\cdot 0+1^2\over 2}\\
{(1+1)^2\over 2^2}&=&{1^2+2\cdot 1+1^2\over 2^2}\\
{(2+1)^2\over 2^3}&=&{2^2+2\cdot 2+1^2\over 2^3}\\
&\vdots &\\
{((n-1)+1)^2\over 2^{n}}&=&{(n-1)^2+2\cdot (n-1)+1^2\over 2^{n}}\\
{(n+1)^2\over 2^{n+1}}&=&{n^2+2\cdot n+1^2\over 2^{n+1}}\end{eqnarray*}$