bobcantor1983
New member
- Joined
- Oct 1, 2013
- Messages
- 3
Let a function f(x) be differentiable at a point x = a and f'(a) = 1. Find the limit
\(\displaystyle \lim_{n\to\infty}n[f(a + \frac{1}{n}) + f(a + \frac{2}{n}) + ... + f(a + \frac{100}{n}) - 100f(a)]\).
I can write it as a series:
\(\displaystyle n[(\sum\limits_{k = 1}^{100} f(a + \frac{k}{n})) - 100f(a)]\);
but I am not sure where to go from there...thoughts?
\(\displaystyle \lim_{n\to\infty}n[f(a + \frac{1}{n}) + f(a + \frac{2}{n}) + ... + f(a + \frac{100}{n}) - 100f(a)]\).
I can write it as a series:
\(\displaystyle n[(\sum\limits_{k = 1}^{100} f(a + \frac{k}{n})) - 100f(a)]\);
but I am not sure where to go from there...thoughts?