To find the sum of the given series, we can simplify each term and then add them together.

The first term is 1/(1+2) = 1/3.
The second term is 1/(1+2+3) = 1/6.
The third term is 1/(1+2+3+4) = 1/10.

We can see a pattern emerging: the denominator of each term is the sum of the first n natural numbers. So, the nth term can be written as 1/(n(n+1)/2).

Now, let's find the sum of the series:

S = 1/3 + 1/6 + 1/10 + ... + 1/(n(n+1)/2) + ...

To find the sum, we need to find the value of n. In this case, n = 20.

S = 1/3 + 1/6 + 1/10 + ... + 1/(20(20+1)/2)

Simplifying the denominator, we get:

S = 1/3 + 1/6 + 1/10 + ... + 1/(20*21/2)

S = 1/3 + 1/6 + 1/10 + ... + 1/(420/2)

S = 1/3 + 1/6 + 1/10 + ... + 1/210

Now, we can find the sum by adding the terms:

S = 1/3 + 1/6 + 1/10 + ... + 1/210

S = 0.333 + 0.167 + 0.1 + ... + 0.005

S ≈ 1.549

Therefore, the sum of the given series is approximately 1.549.