What is the sum of the geometric progression?

If the geometric progression is finite and the number of its elements is n, then its sum is calculated by the formula:

S = b1 * (q ^ (n) – 1) / (q – 1),

where S is the sum itself, b1 is the first term of the sequence, q is the denominator of the geometric progression, which is equal to the quotient of dividing the second term of the progression by the first, n is the number of elements of the geometric progression.

If a geometric progression is infinitely decreasing and the first term of this progression and its denominator are known, then the sum of such a geometric progression is equal to:

S = b1 / (1 – q), where q ≠ 1.