how many ways to make change for n dollars using pennies and nickels?
i.e.
what is the coefficient of the x^100n term in
(1+x+x^2+...+x^100n) * (1+x^5+x^10+...+x^100n)?
for the sake of clarity, I rewrote the sums as finite geometric series using sigma notation. by inspection one can see (i think) that the coefficient of x^100n in the above product would be
1 + 20n ways
have i done this correctly?