Going back once more to the original problem of finding a formula to compute the n triangular number.
T(n)=1+2+3+ ... +n
Triangular numbers suggest by their name the idea of geometry and it should
be interesting to try apply some geometric reasoning to solve the problem.
As we explained in the first lecture triangular numbers are obtained when
we arrange a number of stones in an equilateral triangular shape.
It just happens that it is very convenient for us to re arrange
those stones in another triangular shape.
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