Problem 52729. Easy Sequences 21: Combinatorial Summations

Created by Ramon Villamangca

Solve Later

{"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:rPr><w:b/></w:rPr><w:t>Create the function S(n), defined by the following summation</w:t></w:r><w:r><w:t>:</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>                               </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"60\"/><w:attr w:name=\"width\" w:val=\"224\"/><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 symbol </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"22\"/><w:attr w:name=\"width\" w:val=\"15\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml><w:r><w:t> is the combination function ('nchoosek(a,b)' in MATLAB). 'S(n)' always yields an integer value,  if 'n' is a positive integer. Present the output modulo 1234567.</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:rPr><w:b/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> S(n) may have positive or negative values. Therefore, please use the 'mod' function instead of the 'rem' function to ensure the result would be a positive modulus.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.gif","relationshipId":"rId1"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image2.gif","relationshipId":"rId2"}]},{"partUri":"/media/image1.gif","contentType":"image/gif","content":"data:image/gif;base64,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","relationship":null},{"partUri":"/media/image2.gif","contentType":"image/gif","content":"data:image/gif;base64,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","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: 20.440000534057617px; 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: normal; text-decoration: none; white-space: normal; "><div style="block-size: 205px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><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="font-weight: bold; ">Create the function S(n), defined by the following summation</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="">:</span></span></div><div style="block-size: 66px; 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="">                               </span></span><img class="imageNode" width="224" height="60" style="vertical-align: baseline;width: 224px;height: 60px" src="data:image/gif;base64,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" data-image-state="image-loaded"></div><div style="block-size: 49px; 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 symbol </span></span><img class="imageNode" width="15" height="22" style="vertical-align: baseline;width: 15px;height: 22px" src="data:image/gif;base64,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" data-image-state="image-loaded"><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=""> is the combination function ('nchoosek(a,b)' in MATLAB). 'S(n)' always yields an integer value,  if 'n' is a positive integer. Present the output modulo 1234567.</span></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="font-weight: bold; ">NOTE:</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=""> S(n) may have positive or negative values. Therefore, please use the 'mod' function instead of the 'rem' function to ensure the result would be a positive modulus.</span></span></div></div></div>

Solve

Solution Stats

12 Solutions
6 Solvers

Last Solution submitted on Nov 24, 2022

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

William on 19 Sep 2021

Almost got it, but not quite!

Ramon Villamangca on 19 Sep 2021

Hi William, you are right. The sign should only be negative when n = 2. Thanks.

Rafael S.T. Vieira on 24 Nov 2022

Tip: This problem is not solved using combinations or factorials.

Rafael S.T. Vieira on 24 Nov 2022

S(20) = 177547, you're welcome.

Problem Recent Solvers6

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 52729. Easy Sequences 21: Combinatorial Summations

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author91

Problem Tags

Community Treasure Hunt

Problem 52729. Easy Sequences 21: Combinatorial Summations

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers6

Suggested Problems

More from this Author91

Problem Tags

Community Treasure Hunt

Players

WeChat