Difference between revisions of "User:Pifinity"

 
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== Description of pifinity ==  
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= pifinity's problem set =
<math>\text{Welcome to pifinity's page. pifinity is a wonderful user who participates in class, and the community. pifinity \emph{loves} math.}</math>
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<b>Welcome to pifinity's problem set! This page contains problems created by pifinity. Please do not edit this page.</b>
== pifinity's master expression ==
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== Finalized Problems ==
<math>4 + x + 56^2 - 56 \cdot (23 + 33) \div 39 \prod 56 \times 6905\%_5 \coprod 34 \angle 34 \underarc{ 567} \cdot \omega 45</math>
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==== Problem I ====
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Evaluate <math>\frac{48}{32} + \frac{24}{16}.</math>
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==== Solution I ====
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Simplify; no denominator conversion needed: <cmath>\frac{48}{32} + \frac{24}{16}=\frac{3}{2} + \frac{3}{2} = \boxed{3}.</cmath>
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== Unconfirmed Problems ==
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==== Problem ====
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What is the <math>``\,?\,"</math> term? <cmath>(100-96)+100+(96-92)+94+(92-88)+88+\hdots+?+(4-0)</cmath>
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==== Solution ====
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We first wish to find the number of "telescoping" terms. The first one is <math>100</math> minus something, so we can label it <math>\tfrac{100}4=25.</math> The last term is <math>4</math> minus something, so we can label it <math>\tfrac{4}4=1.</math> Thus there are <math>25-(4-1)=22</math> terms. Therefore, there are 21 gaps between the terms in parentheses. Since there is one less of the terms not in parentheses, then there are 20 gaps between these terms in total. And since <math>6</math> is subtracted each time for the terms not in parentheses, then we have to subtract <math>6\times20=120</math> from <math>100</math>: <cmath>100-120=\boxed{-20}.</cmath>
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== Unsolved Problems ==
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<b>No Unsolved Problems.</b>
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= =
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<cite><sub>This page has 12 official edits. The last edit was on 12:09, May 18, 2018.</sub></cite>

Latest revision as of 15:09, 18 May 2018

pifinity's problem set

Welcome to pifinity's problem set! This page contains problems created by pifinity. Please do not edit this page.

Finalized Problems

Problem I

Evaluate $\frac{48}{32} + \frac{24}{16}.$

Solution I

Simplify; no denominator conversion needed: \[\frac{48}{32} + \frac{24}{16}=\frac{3}{2} + \frac{3}{2} = \boxed{3}.\]


Unconfirmed Problems

Problem

What is the $``\,?\,"$ term? \[(100-96)+100+(96-92)+94+(92-88)+88+\hdots+?+(4-0)\]

Solution

We first wish to find the number of "telescoping" terms. The first one is $100$ minus something, so we can label it $\tfrac{100}4=25.$ The last term is $4$ minus something, so we can label it $\tfrac{4}4=1.$ Thus there are $25-(4-1)=22$ terms. Therefore, there are 21 gaps between the terms in parentheses. Since there is one less of the terms not in parentheses, then there are 20 gaps between these terms in total. And since $6$ is subtracted each time for the terms not in parentheses, then we have to subtract $6\times20=120$ from $100$: \[100-120=\boxed{-20}.\]

Unsolved Problems

No Unsolved Problems.

This page has 12 official edits. The last edit was on 12:09, May 18, 2018.

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