User:Whiteheadj/Square Number

The n+1th square number can be calculated from the nth square number by this formula:

$n^{2}+2n+1$ .

This is calculated by:

$(n+1)^{2}$

$=(n+1)(n+1)$

(multiply out the brackets)

$=n^{2}+n+n+1^{2}$

(simplify)

$=n^{2}+2n+1$

This can be proved because as it details a way to find the next square number, if it works for $1^{2}$ and for $2^{2}$, then it has to work for all other positive numbers.