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Would you say that the value of the infinite sum 1/2 + 1/4 + 1/8 + ... is 1 or that it is an unknown number? The probability that a random number uniformly dra
by kgwgk 7y ago
Would you say that the value of the infinite sum 1/2 + 1/4 + 1/8 + ... is 1 or that it is an unknown number?
The probability that a random number uniformly drawn from the real line is between 42 and 43 is zero in the same way that “the probability that a random real number selected uniformly from the interval [0 1] is pi/4” is zero.
- speedplane 7y ago> Would you say that the value of the infinite sum 1/2 + 1/4 + 1/8 + ... is 1 or that it is an unknown number? Integral of 1/2^n ... got that no problem. I took AB Calculus in high school, three semesters of calculus in college, and a bunch of calculus heavy linear algebra. I’m certain that I knew how to integrate that thing at some point... it’s pretty sad that now I can only stare at it blankly and at best lean heavily on Wikipedia to find an answer.
- kgwgk 7y agoWhat I wrote is an infinite series and it’s much simpler to solve than the integral: https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_⋯ https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%...
- speedplane 7y agoHa, yup, citing a Wikipedia article too. At least I’m not alone.