Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2022 SSMO Accuracy Round Problems/Problem 10

Revision as of 13:04, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let<cmath>S=\sum^{\infty}_{k=5}2^{-10k}\dbinom{2k}{10}.</cmath>Then the value of <math>S</math> can be expressed as <math>\frac mn</math>, where <math>m</math> and...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let\[S=\sum^{\infty}_{k=5}2^{-10k}\dbinom{2k}{10}.\]Then the value of $S$ can be expressed as $\frac mn$, where $m$ and $n$ are relatively prime positive integers. Find the largest positive integer $a$ such that $2^a\mid mn$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_SSMO_Accuracy_Round_Problems/Problem_10&oldid=207304"