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).

}

This space is here to avoid seeing the answers before trying the problem!

}

If you enjoy using this website then please consider making a donation - every little helps :-)

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.