To find the value of s, we can first simplify the expression:

s = 3/1 + 3/1+2 + 3/1+2+3 + .....+ 3/1+2+3+....+100

Notice that the denominator of each term is the sum of consecutive positive integers. We can rewrite the expression as:

s = 3/1 + 3/2 + 3/3 + .....+ 3/100

Now, we can factor out 3 from each term:

s = 3(1/1 + 1/2 + 1/3 + .....+ 1/100)

This is a harmonic series, which can be approximated by the natural logarithm function. The sum of the harmonic series up to n terms is approximately ln(n). Therefore, we can approximate the value of s as:

s ≈ 3 * ln(100)

Using a calculator, we find that ln(100) ≈ 4.60517. Therefore:

s ≈ 3 * 4.60517
s ≈ 13.81551

So, the value of s is approximately 13.81551.