Answer is: option2

Solution:

Recognize the form of the Riemann sum

The sum inside the brackets is:

\[ \sum_{i=1}^{20} \frac{i}{10} \]

So the full expression becomes:

\[ \frac{1}{10} \sum_{i=1}^{20} \frac{i}{10} \]

This is of the form:

\[ \sum_{i=1}^{n} f(x_i) \Delta x \]

With:

1. \( \Delta x = \frac{1}{10} \)
2. \( x_i = \frac{i}{10} \)
3. \( f(x) = x \)

Therefore, this is a right Riemann sum approximation for the integral:

\[ \int_0^2 x \, dx \]

Because:

1. The values of \( x_i = \frac{i}{10} \) go from \( \frac{1}{10} \) to \( \frac{20}{10} = 2 \) — 20 subintervals.
2. It approximates the area under \( f(x) = x \) from \( x = 0 \) to \( x = 2 \).

Option - B