Problem Statement

In number theory, Sylvester's sequence is an integer sequence in which each term of the sequence is the product of the previous terms, plus one. Its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions with the same number of terms. Further, the sum of the first k terms of the infinite series of reciprocals provides the closest possible underestimate of 1 by any k-term Egyptian fraction.

Let's start with the solution:

F sylverster(lim)
   V result = [BigInt(2)]
   L 2..lim
      result.append(product(result) + 1)
   R result

V l = sylverster(10)
print(‘First 10 terms of the Sylvester sequence:’)
L(item) l
   print(item)

V s = 0.0
L(item) l
   s += 1 / Float(item)
print("\nSum of the reciprocals of the first 10 terms: #.17".format(s))