Given:
n
$\displaystyle Sigma$ k/(n^2)
k = 1
show that
limit as n-> infinity Sn = integral from 0 -> 1 on (xdx)
by comparing the Reimann sum for the integral to the
series.
can someone walk me through this problem?, thanks
Given:
n
$\displaystyle Sigma$ k/(n^2)
k = 1
show that
limit as n-> infinity Sn = integral from 0 -> 1 on (xdx)
by comparing the Reimann sum for the integral to the
series.
can someone walk me through this problem?, thanks
S=$\displaystyle \int_0^1 xdx=\lim_{n\rightarrow\infty} \sum_{k=0}^n f(x_k)\Delta$ , where $\displaystyle n\Delta=b-a=1$ and $\displaystyle x_k=k\Delta$.
$\displaystyle S=\lim_{n\rightarrow\infty} \sum_{k=0}^n k\Delta^2=\lim_{n\rightarrow\infty} \sum_{k=0}^n \frac k{n^2}$