Sum Of Natural Numbers

Relevant wiki: Sum of n, n², or n³

From the diagram, it is easy to find the total number of yellow squares is half of the rectangle area. The half of the rectangular area= (10x11)/2=55

N(N+1)/2= (10*11)/2=55

(N/2)(n+1)

The answer is $\displaystyle \sum_{n=1}^{10} n = \dfrac{10 × 11}{2} = \boxed{55}$ .

Alternate method:

The number of yellow boxes in each row forms an arithmetic progression with:

$a=1 \quad d=1 \quad n=10 \quad T_n = T_{10} = 10\\ S_{10} = \dfrac{10}{2}\left(1+10\right) = 5 \times 11 = \boxed{55}$