Difference between revisions of "G285 2021 Fall Problem Set"
Geometry285 (talk | contribs) m |
Geometry285 (talk | contribs) m (→Problem 8) |
||
Line 8: | Line 8: | ||
==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 can be represented as
, where
and
are relatively prime. Find
.