The sum of the series 1 + (1 + 3) + (1 + 3 + 5) + ……. + (1 + 3 + …… + 15 + 17) is

This is a series of sums of odd numbers. The sum of the first n odd numbers is n^2.

The series is:

1 + (1 + 3) + (1 + 3 + 5) + ……. + (1 + 3 + …… + 15 + 17)

This can be rewritten as:

1^2 + 2^2 + 3^2 + ... + 9^2

This is the sum of the squares of the first 9 natural numbers.

The formula for the sum of the squares of the first n natural numbers is n(n + 1)(2n + 1) / 6.

Substituting n = 9 into the formula gives:

9(9 + 1)(29 + 1) / 6 = 910*19 / 6 = 285

So, the sum of the series 1 + (1 + 3) + (1 + 3 + 5) + ……. + (1 + 3 + …… + 15 + 17) is 285.