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
Idk how to explain calculus like you’re five but I’ll try.
Basically, it doesn’t actually become 1. Instead the addition of 1/2 + 1/4 + 1/8 + . . . . . 1/2n becomes infinitely close to 1, to the point where it’s pretty much just 1.
Imagine eating a cupcake, but leaving behind a crumb. You’ve still eaten a cupcake. Similarly, this sum is still considered 1 even though it’s not quite 1.
In calculus or precalculus this would be a limits problem. Given that you’re trying to find the sum of 1/2 + 1/4 + 1/8 + . . . 1/2n, as n approaches infinity, the sum approaches 1.
I hope this helped? If it didn’t I’m sorry and someone better at math than me will probably come by and explain better
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