How does the sum of 1/2 + 1/4 + 1/8 etc. (Halves each time) eventually become 1? I understand it’s infinite but surely it still wouldn’t work?
In: Mathematics
Other comments are correct, regarding the calculus proofs. But you can kind of think of it like this.
While the numbers you add up are getting infinitely smaller, you are adding them up infinite times.
It kinda is easier to imagine things as infinitely small rather than things as being done an infinite amount of time. However, the maths equation doesn’t care about that, the two infinite processes are working against each other and kind of cancel out to a standard number that we are comfortable with.
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