perplexus.info :: Just Math : half power

half power (Posted on 2023-10-16)

Consider the following function f(x) = (1/2)^x - (1/2)^x+1.

Evaluate the infinite sum f(1) + f(2) + f(3) + f(4) +...

No Solution Yet Submitted by Danish Ahmed Khan

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Difficulty 1 (spoiler)

Comment 2 of 2 |

f(1) + f(2) + f(3) + f(4) +... = 1/2

All the terms after (1/2)^1 cancel out

Posted by Steve Herman on 2023-10-16 07:50:40

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