2010 UNCO Math Contest II Problems/Problem 8

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.

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

2010 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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