Find a, b, c
Posted: Sat May 17, 2008 10:53 am
Let f be a real function defined on [0;1] which is \( C^3 \) (it means that f''' there exists and it is continous).
Find a, b, c such that
\( \frac{1}{n}\sum_{k=1}^{n}f(k/n)=a+\frac{b}{n}+\frac{c}{n^2}+\frac{u(n)}{n^2} \)
with u(n) tend to zero when n tend \( \infty \).
Find a, b, c such that
\( \frac{1}{n}\sum_{k=1}^{n}f(k/n)=a+\frac{b}{n}+\frac{c}{n^2}+\frac{u(n)}{n^2} \)
with u(n) tend to zero when n tend \( \infty \).