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]

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- Dec 5th 2009, 07:54 PMbinkypooriemann integration help
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] - Dec 6th 2009, 12:45 AMtonio
- Dec 6th 2009, 01:53 PMbinkypoo
please excuse me, I should have used latex,

I made x <= 1/n, which reads

$\displaystyle x \leq 1/n$

sorry. - Dec 6th 2009, 01:59 PMtonio
- Dec 6th 2009, 02:58 PMbinkypoo
$\displaystyle f(x)=\left\{

\begin{array}{lr}

\frac{1}{n} & : \frac{1}{n+1}< x\leq \frac{1}{n}\\

0 & : x=0

\end{array}\right.$ - Dec 6th 2009, 02:59 PMPlato
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 $\displaystyle f(x) = \left\{ {\begin{array}{rl} 0 & {,x = 0} \\ {\frac{1}{n}} & {,x \in \left( {\frac{1}{{n + 1}},\frac{1}{n}} \right]} \\ \end{array} } \right.$