perplexus.info :: Just Math : Digital sum

Digital sum (Posted on 2005-08-20)

For each positive integer n, let A(n) be the number of digits in the binary representation of n, and let B(n) be the number of ones in the binary representation of n. What is the value of S:

S = (1/2)^[A(1)+B(1)] + (1/2)^[A(2)+B(2)] + (1/2)^[A(3)+B(3)] + ...

See The Solution Submitted by pcbouhid

Rating: 4.4000 (5 votes)

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Puzzle Answer

Comment 8 of 8 |

The required value of the given expression is 1.

**** What an interesting but mind-boggling problem !

I will strive to derive an independent analytical explanation of my own to this very absorbing puzzle !!

Edited on May 26, 2022, 11:02 pm

Posted by K Sengupta on 2022-05-26 23:00:31

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