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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Puzzle Solution

| Comment 1 of 2

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

= (1/2) - (1/2)^2 + (1/2)^3 - (1/2)^4+...

= (1/2+ 1/8+ 1/32+.....) - (1/4+ 1/16 + 1/64+....)

= (1/2)/(1- 1/4) - (1/4)/(1-1/4)

= (1/2)/(3/4) - (1/4)/(3/4)

= (1/2 -1/4)/(3/4)

= (1/4)/(3/4)

= 1/3

Posted by K Sengupta on 2023-10-16 07:21:27

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