(1-1/2)(1-1/3)(1-1/4). . . (1-1/n)=1/n
How do i start this?
Okay, we have the "base" case:
So this works for n = 2.
Let's assume this works for some n = k, that is that
Let's see what the n = k + 1 case says:
By hypothesis, the product of all but the last factor is simply 1/k, so:
Simplifying a bit:
So it is true for n = 2, thus it is true for n = 3, 4, ...