does this apply only for terms that are less than 1 eg 1 + 1/2 + 1/4…. or does this apply to all ap/gp. I remember studying this, but it’s been so long I remember only the gist.
In: 248
There’s a subtlety that is being missed in most answers here. An “infinite sum” is not the same thing as a finite sum. I.e. 1+1/2+1/4+… is not the same kind of thing as 1+2+3. It doesn’t follow from the normal rules of addition that one learns in primary school that the infinite sum just given sums to 2.
Instead, what happens is that mathematicians *define* an “infinite sum”, using some moderately sophisticated maths to specify what the actual value of the sum will be when you evaluate it. Of course, they choose sensible rules so that the outcome makes some intuitive sense. See other answers for the actual intuition in play.
Latest Answers