How to calculate the terms of a geometric progression?

Question

Mathematics

The sum of the terms of a geometric progression with a denominator of 2 is 589952.
How to find all the terms of a geometric progression, knowing only the above data?

Answer 1

589952 == 2^19 + 2^16 + 2^7

Answer 2

There are two options. 1) What horrible whole members; 2) Consecutive integer members. Longclaps answered the question "what horrible members" (without a solution) , I will answer the second one.
589952 = a ₀ ( ²ⁿ − 1).
And now we divide our number into factors: 589952 \u003d 2 ⁷ ∙ 11 ∙ 419.
Twos can only go to the first term a ₀ . And with 419 and 11 - neither each of them, nor their product is similar to 2 ⁿ − 1.
So the only answer is a single term equal to 589952.
Are you sure you rewrote the number 589952?
If the terms are consecutive, but not integers, there may be ∞ answers - for example, 10 terms, the first of which is ⁵⁸⁹⁹⁵² /₁₀₂₃ .