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Little power sum (Posted on 2024-11-15)

Find the sum of all positive integers of the form 2^r*3^s, where r and s are nonnegative integers that do not exceed 4.

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Solution

Comment 4 of 4 |

Why is anyone using a computer? This is Pencil and Paper!

The trick here is to realize the sum of all 25 terms can be generated from a product of a pair of five term sums.

(2^0 + 2^1 + 2^2 + 2^3 + 2^4) * (3^0 + 3^1 + 3^2 + 3^3 + 3^4)

The two multiplicands are geometric series, so the expression simplifies into (2^5 - 1) * (3^5 - 1) / 2 = 31*242/2 = 3751.

Edited on November 15, 2024, 4:58 pm

Posted by Brian Smith on 2024-11-15 10:53:56

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