Question 24-19 from Spivak's calclus:
I have a small issue with the solution to 24-19 in Spivak's calculus presented below:
Although the part in highlight makes intuitive sense to me, I can't seem to express the logic rigorously. In particular I don't see how we can get to an inequality with an infinite number of terms from the inequality with only a finite number of turns. Can anyone present how the highlight is derived more clearly?