I need help with the following:
suppose that f:[0,1]-->R is defined by:
f(x)=1/n if 1/(n+1) < x <= 1/n
and 0 if x=0.
Verify that f is riemann integrable on the interval [0,1]
The collection of intervals $\displaystyle \left\{ {\left( {\frac{1}{{n + 1}},\frac{1}{n}} \right]:n \in \mathbb{Z}^ + } \right\}$ partitions $\displaystyle (0,1]$.
So the function is $\displaystyle f:[0,1]\mapsto [0,1]$ by $\displaystyle f(x) = \left\{ {\begin{array}{rl} 0 & {,x = 0} \\ {\frac{1}{n}} & {,x \in \left( {\frac{1}{{n + 1}},\frac{1}{n}} \right]} \\ \end{array} } \right.$