Difference between revisions of "G285 2021 Fall Problem Set"
Geometry285 (talk | contribs) m |
Geometry285 (talk | contribs) m (→Problem 8) |
||
(2 intermediate revisions by the same user not shown) | |||
Line 8: | Line 8: | ||
==Problem 8== | ==Problem 8== | ||
− | + | Find <cmath>\sum_{a=0}^{\infty} \sum_{b=0}^{\infty} \sum_{c=0}^{\infty} \sum_{d=0}^{\infty} \frac{a+2b+3c}{4^{(a+b+c+d)}}</cmath> | |
+ | |||
+ | <cmath>\textbf{(A)}\ \frac{16}{27} \qquad \textbf{(B)}\ \frac{32}{27} \qquad \textbf{(C)}\ \frac{64}{27} \qquad \textbf{(D)}\ \frac{128}{27} \qquad \textbf{(E)}\ \frac{256}{27}</cmath> | ||
[[G285 2021 Fall Problem Set Problem 8|Solution]] | [[G285 2021 Fall Problem Set Problem 8|Solution]] |
Latest revision as of 21:43, 18 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
Find