Here is a small challenge for your entertainment and gratification. For any natural number n, let f(n) denote the sum of the numbers from 1 to n. Thus f(1)=1, f(2)=1+2=3, f(3)=1+2+3=6, f(100)=1+2+3+…+100=5050, etc.
It turns out that f is a polynomial of degree 2 in n. Figure out the coefficients of f:
f(n)=
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