I was wondering if anyone could help me with the following problems.
I am working with the function f(x) = ? ({n!*x})/n! where n goes from 0 to infintity and {x} = distance from x to the nearest integer.
a) I need to use the comparison test to show that f(x) converges. I know that I can compare it to ? 1/n!
b) I need to show that f(x) is continuous at x=a. I know that I can chose an N so that ? ({n!*x})/n! < ? (n goes from N+1 to infinity), and then use
? ({n!*x})/n! - ? ({n!*a})/n! (n goes from N to infinity).
Thanks
I am working with the function f(x) = ? ({n!*x})/n! where n goes from 0 to infintity and {x} = distance from x to the nearest integer.
a) I need to use the comparison test to show that f(x) converges. I know that I can compare it to ? 1/n!
b) I need to show that f(x) is continuous at x=a. I know that I can chose an N so that ? ({n!*x})/n! < ? (n goes from N+1 to infinity), and then use
? ({n!*x})/n! - ? ({n!*a})/n! (n goes from N to infinity).
Thanks