Problem 57447. Compute a nested cube root

Created by ChrisR

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Consider the quantity </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\"/></w:customXmlPr><w:r><w:t>y = (a+(a+(a+(a+\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}</w:t></w:r></w:customXml><w:r><w:t>. Write a function to compute </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y\"/></w:customXmlPr><w:r><w:t>y</w:t></w:r></w:customXml><w:r><w:t> without using loops or recursion. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; "><div style="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; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; 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; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; "><span style="">Consider the quantity </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}" style="width: 249px; height: 19.5px;" width="249" height="19.5"></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; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; "><span style="">. Write a function to compute </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">y</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; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; "><span style=""> without using loops or recursion. </span></span></div></div></div>

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Last Solution submitted on May 30, 2023

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Problem 57447. Compute a nested cube root

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Problem 57447. Compute a nested cube root

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