What is the difference between summing 9/10+9/100+9/1000+.... and the summation process that takes place in an integral? For example, if f(x)=1 and we compute the integral from 0 to 1, the answer is 1. One can argue that we are calculating the area of a square with side 1 unit. Is there a way to show how 0.999... ties into all of this? Evidently the integral by definition is the limit of an infinite average but 0.999... is not an average.
2006-09-07 04:33:18 · 2 answers · asked by Marianne M 1 in Science & Mathematics ➔ Mathematics
The difference is that the integral is the sum of an area. 0.999... is neither an area nor a distance. I don't see any similarity.
2006-09-07 04:48:28 · answer #1 · answered by Anonymous · 0⤊ 1⤋
Yes, they are 'kinda' the same thing. In an integral you're calculating the limit of a number of areas as the number of areas goes to â and the area of each one goe to 0.
.9 +.09+.009... is the limit of a series as the number of terms goes to â and the value of the terms goes to 0.
Doug
2006-09-07 11:41:47 · answer #2 · answered by doug_donaghue 7 · 0⤊ 1⤋