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Type: Multiple-Choice
Category: Polynomials and Rational Expressions
Standards: HSA-APR.C.5
Author: nsharp1
Created: a month ago

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# Polynomials and Rational Expressions Question

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## Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5

Euler's number, $e$, is an irrational number (like $pi$). You can approximate $e$ with the formula $(1+1/n)^n$, such that the approximation improves as $n$ approaches infinity. Which of the following is an equivalent formula, using the Binomial Theorem and the fact that $({:(n),(k):}) (1/n)^k = 1/(k!)$ as $n$ approaches infinity?
1. $sum_{k=0}^n 1/(k!)$
2. $sum_{k=0}^n (k^n)/(k!)$
3. $sum_{k=0}^n (n!)/(k!)$
4. $sum_{k=0}^n (n-k)/(k!)$
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