Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 7, 2011"

Latest revision as of 17:15, 7 July 2011

This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it.

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 ==Solution==
 {{potd_solution}}
-The <math>k</math>-th term in the sequence is <math>\dfrac{10^k - 1}{9}</math>. By using basic summation properties, and the formula for the sum of a [[geometric sequence]], the desired sum is:
-<math>\sum_{k=1}^{n}\dfrac{10^k - 1}{9} = \dfrac{1}{9}\sum_{k=1}^{n}10^k - \dfrac{1}{9}\sum_{k=1}^{n}1 = \dfrac{10^{n+1}-10}{81} - \dfrac{n}{9} = \dfrac{10^{n+1}-9n-10}{81}</math>.