Henry Ernest Dudeney/Puzzles and Curious Problems/229 - Geometrical Progression

Puzzles and Curious Problems by Henry Ernest Dudeney: $229$

Geometrical Progression

Write out a series of whole numbers in geometrical progression, starting from $1$,

so that the numbers should add up to a square.

Thus, $1 + 2 + 4 + 8 + 16 + 32 = 63$.

But this is one short of being a square.

I am only aware of two answers in whole numbers, and these will be found easy to discover.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $229$. -- Geometrical Progression
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $243$. Geometrical Progression