Mathematics

Problem

Let

a<b

and

\Delta x=\dfrac{b-a}{n}

with partition points

x_k=a+k\Delta x

for

k=0,1,\ldots,n

. Denote by

L_n

and

R_n

the rectangular sums that use left and right endpoints, respectively. Write the average

\dfrac{L_n+R_n}{2}

as a single expression in sigma notation.