User:Whiteheadj/Square Number
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The n+1th square number can be calculated from the nth square number by this formula:
n2 + 2n + 1 .
This is calculated by:
(n + 1)2
= (n + 1)(n + 1)
(multiply out the brackets)
= n2 + n + n + 12
(simplify)
= n2 + 2n + 1
This can be proved because as it details a way to find the next square number, if it works for 12 and for 22, then it has to work for all other positive numbers.
