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Type: Multiple-Choice
Category: Polynomials and Rational Expressions
Level: Grade 12
Standards: HSA-APR.C.5
Author: nsharp1
Created: 6 years ago

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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?

$sum_{k=0}^n 1/(k!)$
$sum_{k=0}^n (k^n)/(k!)$
$sum_{k=0}^n (n!)/(k!)$
$sum_{k=0}^n (n-k)/(k!)$