Difference between revisions of "2008 UNCO Math Contest II Problems/Problem 9"

Revision as of 02:03, 13 January 2019

Let $C_n = 1+10 +10^2 + \cdots + 10^{n-1}.$

(a) Prove that $9C_n = 10^n -1.$

(b) Prove that $(3C_3+ 2)^2 =112225.$

(c) Prove that each term in the following sequence is a perfect square: $25, 1225, 112225, 11122225, 1111222225,\ldots$

(a) $\frac{10^n-1}{9}$ (b) $112,225$ (c) $11,122,225$

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 == Solution ==
-{{solution}}
+(a) <math>\frac{10^n-1}{9}</math>  (b) <math>112,225</math>   (c) <math>11,122,225</math>
 == See Also ==

2008 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNCO Math Contest Problems and Solutions