/categories/problems/Recent content in Problems on Lowell Math SocietyHugo -- gohugo.ioen© 2026 Lowell Math SocietySat, 09 May 2026 00:00:00 +0000/problems/2026-01/Sat, 09 May 2026 00:00:00 +0000/problems/2026-01/<p> <!-- for above, change YYYY to current year and NN to current problem set --></p> <h2 class="relative group"><a href="/solutions/2026-01/" >Solutions Page</a> <!-- change YYYY to current year and NN to current problem set --> <div id="solutions-page" class="anchor"></div> <span class="absolute top-0 w-6 transition-opacity opacity-0 -start-6 not-prose group-hover:opacity-100 select-none"> <a class="text-primary-300 dark:text-neutral-700 !no-underline" href="#solutions-page" aria-label="Anchor">#</a> </span> </h2> <h2 class="relative group">Problem 1 <div id="problem-1" class="anchor"></div> <span class="absolute top-0 w-6 transition-opacity opacity-0 -start-6 not-prose group-hover:opacity-100 select-none"> <a class="text-primary-300 dark:text-neutral-700 !no-underline" href="#problem-1" aria-label="Anchor">#</a> </span> </h2> <p>Evaluate the following: </p> $$ 2-3+10-15+26-35+50-63+82-99 \cdots +2026 $$ <h3 class="relative group">Hints <div id="hints" class="anchor"></div> <span class="absolute top-0 w-6 transition-opacity opacity-0 -start-6 not-prose group-hover:opacity-100 select-none"> <a class="text-primary-300 dark:text-neutral-700 !no-underline" href="#hints" aria-label="Anchor">#</a> </span> </h3> <details> <summary>Hint 1</summary> The pattern is: $$ t_n = (-1)^{n-1}n^2+1 $$ </details> <details> <summary>Hint 2</summary> Can you do something about the \(1\) term? What does the sum look like visually without the 1 term? </details> <h2 class="relative group">Problem 2 <div id="problem-2" class="anchor"></div> <span class="absolute top-0 w-6 transition-opacity opacity-0 -start-6 not-prose group-hover:opacity-100 select-none"> <a class="text-primary-300 dark:text-neutral-700 !no-underline" href="#problem-2" aria-label="Anchor">#</a> </span> </h2> <p>If the function \(f(x)\) is quadratic, \(f(0)=2025\), \(f(1)=2026\), and \(f(2)=1984\), then what is \(f(10)\)</p>