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Type: Multiple-Choice
Category: Polynomials and Rational Expressions
Level: Grade 12
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, [math]e[/math], is an irrational number (like [math]pi[/math]). You can approximate [math]e[/math] with the formula [math](1+1/n)^n[/math], such that the approximation improves as [math]n[/math] approaches infinity. Which of the following is an equivalent formula, using the Binomial Theorem and the fact that [math]({:(n),(k):}) (1/n)^k = 1/(k!) [/math] as [math]n[/math] approaches infinity?
  1. [math]sum_{k=0}^n 1/(k!)[/math]
  2. [math]sum_{k=0}^n (k^n)/(k!) [/math]
  3. [math]sum_{k=0}^n (n!)/(k!) [/math]
  4. [math]sum_{k=0}^n (n-k)/(k!)[/math]
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