Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 8"
(Created page with "== Problem == Simplify <math>(3^1+1)(3^2+1)(3^4+1)(3^8+1)(3^{16}+1)\cdots (3^{1024}+1)</math>, using exponential notation to express your answer. Generalize this result. == So...") |
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== Solution == | == Solution == | ||
| + | Let the product = <math>P</math>. Then | ||
| + | <math>(3-1)P=3^{2048}-1\implies</math> | ||
| + | <math>P=\frac{3^{2048}-1}{2}</math> | ||
== See also == | == See also == | ||
| − | {{ | + | {{UNCO Math Contest box|year=2010|n=II|num-b=7|num-a=9}} |
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Latest revision as of 20:12, 12 October 2015
Problem
Simplify 
, using exponential notation to
express your answer. Generalize this result.
Solution
Let the product = 
. Then
See also
| 2010 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| 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 | ||
