What is the summation of 1/x - 1/(x+1) from x=1 to x=infinity?
In other words, what does the series converge to?
2007-12-13 08:35:21 · 2 answers · asked by Not Quite Agnostic 2 in Science & Mathematics ➔ Mathematics
Sorry, What does the sum of the series converge to?
2007-12-13 08:49:01 · update #1
well it'll converge to zero. I cannot seem to work it out using the formula sum to infinity = a/r cos the steps aren't equal. But cos the terms are constantly getting smaller its getting closer to zero as n gets closer to infinity
2007-12-13 08:44:15 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Look at it this way. For x = 1, you take 1/1 = 1 and you subtract 1/(1+1) = 1/2. For x = 2, you add 1/2 and subtract 1/(2+1) = 1/3. For x = 3, you add 1/3 and subtract 1/4. For each increment of x, you add in a fraction that is equal to the fraction you just subtracted, and then you subtract a smaller fraction. So for the sum from x = 1 to n, all you really have is the very first fraction, 1/1 = 1, with 1/n subtracted from it. As x goes to infinity, 1/x goes to zero, so you're just left with 1. The sum of the series converges to 1.
2007-12-16 15:20:06 · answer #2 · answered by DavidK93 7 · 0⤊ 0⤋