Problem 56000. Estimating Euler's (Oi-ler-z) Number

Created by Ben Placek

Solve Later

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Repeat this </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> times, then calculate the estimate of Euler's number by computing the mean of those counts.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The more iterations calcualted, the closer the approximation should be.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"333\"/><w:attr w:name=\"width\" w:val=\"446\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The input to your function should be the number of iterations of the algorithm to perform (N) and the output should be the estimate of Euler's 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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.math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"><span style="">Euler's number is an irrational constant given by </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="103.5" height="18" style="width: 103.5px; height: 18px;"></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">Starting with </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">x=0</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">, count the number of times you can add a uniformly distributed random number to </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">x</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> before it equals or exceeds 1. Repeat this </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">N</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""> times, then calculate the estimate of Euler's number by computing the mean of those counts.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The more iterations calcualted, the closer the approximation should be.</span></span></div><div style="block-size: 339px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" width="446" height="333" style="vertical-align: baseline;width: 446px;height: 333px" src="data:image/png;base64,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" data-image-state="image-loaded"></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The input to your function should be the number of iterations of the algorithm to perform (N) and the output should be the estimate of Euler's number.</span></span></div></div></div>

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Problem 56000. Estimating Euler's (Oi-ler-z) Number

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Problem 56000. Estimating Euler's (Oi-ler-z) Number

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