Triangular \ Square number
Hi all - can someone please help with the following
Let Tm, Tn be triangular numbers.
I need to show that (2m+1)^2*Tn + Tm is also triangular
Now,,,,I have tried time and time again to expand the number and then somehow factorise it to make another triangular number , but with no success.
(1) (2m+1)^2 = 4m^2 + 4m + 1
(2) Tn = n(n+1) / 2
(3) Tm = m(m+1) / 2
But trying to multiply (1)*(2) and then add the term for (3) just ends up with a very long result, which I can't factorise.
Any ideas please ??? Thanks a lot if anyone can explain it to me
ps : (2m+1)^2 is of course a square number, S(2m+1), but am not aware of any property for the product of a square number with a triangular number....unless I am missing something??