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Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 8"

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== Solution ==
 
== Solution ==
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Let the product = <math>P</math>. Then
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<math>(3-1)P=3^{2048}-1\implies</math>
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<math>P=\frac{3^{2048}-1}{2}</math>
  
 
== See also ==
 
== See also ==

Latest revision as of 20:12, 12 October 2015

Problem

Simplify $(3^1+1)(3^2+1)(3^4+1)(3^8+1)(3^{16}+1)\cdots (3^{1024}+1)$, using exponential notation to express your answer. Generalize this result.


Solution

Let the product = $P$. Then $(3-1)P=3^{2048}-1\implies$ $P=\frac{3^{2048}-1}{2}$

See also

2010 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
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