Difference between revisions of "G285 2021 Fall Problem Set"
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==Problem 8== | ==Problem 8== | ||
| − | If the value of <cmath>\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^(a+b+c)}</cmath> can be represented as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime. Find <math>m+n</math>. | + | If the value of <cmath>\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^{(a+b+c)}}</cmath> can be represented as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime. Find <math>m+n</math>. |
[[G285 2021 Fall Problem Set Problem 8|Solution]] | [[G285 2021 Fall Problem Set Problem 8|Solution]] | ||
Revision as of 12:38, 11 July 2021
Welcome to the Fall Problem Set! There are 
problems, 
multiple-choice, and 
free-response.
Problem 1
Larry is playing a logic game. In this game, Larry counts 
, and removes the number 
for every 
th move, skipping 
for 
, and then increments 
by one. If 
starts at 
, what is when Larry counts his 
th integer? Assume 
Problem 2
Let 
be a right triangle with right angle at 
, and 
. Let 
denote the intersection of the cevian dropped from onto 
such that 
. If the reflection of point across lies on the circumcircle of as 
, 
, and the circumradius of is an integer, find the smallest possible value of 
.
Problem 8
If the value of ![\[\sum_{a=1}^{\infty} \sum_{b=1}^{\infty} \sum_{c=1}^{\infty} \frac{a+2b+3c}{4^{(a+b+c)}}\]](http://latex.artofproblemsolving.com/8/3/e/83e4f5da4b3b44825dcf84447f1deb0711d88c15.png)
can be represented as 
, where 
and 
are relatively prime. Find 
.
