## 9 Nov 2013

### OEMO 2001 Advanced Q1: Upper Secondary Mathematics Competition Question

Let n be an integer and S(n) be the sum of the 2001 powers of n with exponents 0 through 2000.
That is,
$S(n)=&space;\sum_{k=0}^{2000}&space;{n}^{k}$

Determine the final digit (i.e., the ones-digit) in the decimal expansion of S(n).

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