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?

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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.

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121

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A geometric series that sums to a square

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