Answer
Number of blue stars =1+2+3+...+n = $\frac{n(n+1)}{2}$
Work Step by Step
From the figure, it is evident that
Number of blue stars in ith row = i ....(1)
Number of red stars = number of blue stars ....(2)
Number of rows = n
Number of columns = n+1
Therefore, the total number of blue stars $= 1+2+3+...+n$ (by (1))
And total number of stars = Number of rows$\times$Number of columns = $n(n+1)$
But total number of stars = blue + red = $2\times$ blue (by (2))
By previous two equations,
$2\times$ blue stars = $n(n+1)$
Or, Number of blue stars =1+2+3+...+n = $\frac{n(n+1)}{2}$
