A geometric series that sums to a square

HardBrainteasers~10m

Consider $1 + r + r^2 + \cdots + r^{k}$ where the common ratio $r > 1$ is an integer and there are at least $3$ terms. What is the smallest perfect square achievable as such a sum?

Show hints (2)+

Try integer ratios $r=2,3,\dots$ and $\ge 3$ terms; test each geometric sum for being a square.
$r=3$ gives $1+3+9+27+81=121=11^2$ , and nothing smaller qualifies.

Answer

Reveal answer →

121

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise free Unlock solutions

Asked at: Jane Street, Two Sigma

A geometric series that sums to a square

Answer

Related questions