So the amount you are adding is getting smaller with each iteration, 1/4 is smaller than 1/2, however you are still adding 1/4 on top of the 1/2, and those two are combined, closer to “1” than either of them independently correct? (1/2 +1/4 =1/3. 1/3>1/2)
So if the number gets bigger forever than at some point it will eventually hit “1”, since we already started with “1” the next “1” will be “2”
I hope I’m explaining it well enough, it’s similar to how 3.33(repeating)x3…=10 (though technically for different reasons)
Bender_on_Fire@lemmy.world 1 week ago
I didn’t see the pattern either and had to look it up. Apparently, you can rewrite 1 + 1/(1+2) + 1/(1+2+3)+… as 2(1 - 1/2 + 1/2 - 1/3 +…+1/n - 1/(n + 1)) = 2(1 - 1/(n + 1))
From there, the limit of 2 is obvious, but I guess you just have to build up intuition with infinite sums to see the reformulation.