Problem 52769. Easy Sequences 22: Sum of Proper Fractions

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:t>Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:</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=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>F(10)=\\left \\{ \\frac{1}{2},\\frac{1}{3},\\frac{1}{4},\\frac{1}{5},\\frac{1}{6},\\frac{1}{7},\\frac{1}{8},\\frac{1}{9},\\frac{1}{10},\\frac{2}{3},\\frac{2}{5},\\frac{2}{7},\\frac{2}{9},\\frac{3}{4},\\frac{3}{5},\\frac{3}{7},\\frac{3}{8},\\frac{3}{10},\\frac{4}{5},\\frac{4}{7},\\frac{4}{9},\\frac{5}{6},\\frac{5}{7},\\frac{5}{8},\\frac{5}{9},\\frac{6}{7},\\frac{7}{8},\\frac{7}{9},\\frac{7}{10},\\frac{8}{9},\\frac{9}{10}  \\right \\} </w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Note that '2/4' and '3/9' are not included because they are not in their lowest term, while '7/7' and '8/5' are not included because they are not proper fractions.</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>Write a function 'S(d)', which is the integer part of the sum of 'F(d)'.</w:t></w:r><w:r><w:t>  For the case above, the sum of elements of 'F(10)' is exactly '15.5'. Therefore S(10) = 15.</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: 188px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 94px; transform-origin: 407px 94px; vertical-align: baseline; "><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; 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: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; "><span style="">Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:</span></span></div><div style="block-size: 35px; 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 17.5px; text-align: left; transform-origin: 384px 17.5px; 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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; "><span style="">            </span></span><span style="vertical-align:-15px"><img src="data:image/png;base64,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" style="width: 604px; height: 35px;" width="604" height="35"></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; 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: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; "><span style="">Note that '2/4' and '3/9' are not included because they are not in their lowest term, while '7/7' and '8/5' are not included because they are not proper fractions.</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; 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: 233px 8px; transform-origin: 233px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">Write a function 'S(d)', which is the integer part of the sum of 'F(d)'.</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; perspective-origin: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; "><span style="">  For the case above, the sum of elements of 'F(10)' is exactly '15.5'. Therefore S(10) = 15.</span></span></div></div></div>

Solve

Solution Stats

7 Solutions
4 Solvers

Last Solution submitted on Nov 02, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

David Hill on 23 Sep 2021

Could not figure out how to speed up my code. Ended up having to use a lookup table to speed it up sufficiently.

Ramon Villamangca on 28 Sep 2021

Hi,

There is a shortcut using Mobius Inversion...

Solution Comments

Solution 6597389

2 Comments

2 Comments

Are Mjaavatten on 28 Sep 2021

I too had problems with the time limit for large arguments and had to resort to a few tricks. But my solution is still general.

Ramon Villamangca on 28 Sep 2021

There is a shortcut using Mobius Inversion...

Problem Recent Solvers4

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 52769. Easy Sequences 22: Sum of Proper Fractions

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author53

Problem Tags

Community Treasure Hunt

Problem 52769. Easy Sequences 22: Sum of Proper Fractions

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author53

Problem Tags

Community Treasure Hunt

Players