We can achieve this by using the formula for the sum of an arithmetic series:

Sn = n/2 * (2a + (n-1)d)

where

Sn = Sum of n terms

n = Number of terms =40

a = First term =6

d = Common difference =6

We substitute the values:

Sn = 40/2 * (2*6 + (40-1)6)

= 20 * (12+396)

= 20 * (12+234)

= 20 * 246

= 4920

Therefore, the sum of the first 40 positive integers that are divisible by 6 is 4920.