- I have not thought before that we can project the series to a matrix.

- If we just think of a matrix consisting of 101 columns and 100 rows, calculate the area and divide it by 2, we will have the answer.

- Why?
  - because apparently if we only count 100 * 100, it doesn't count the other half of the diagonal.

- What is we just want to calculate a random series, for example, the sum starting at 50 to 250?

- We will find that now we need to calculate a trapezoid, whose area is:

(50+250)*201/2 = 30150
- Why 201: 250-50+1=201. We see 50 and 250 as index, so we use 250-50+1 to calculate the amount.