Question

if sn, denotes the sum of n terms of a GP whose first term and common ratio are a and r respectively. then S₁+S₂.........+Sn is

Answer 1

The sum of a geometric series can be found using the formula Sn = a * (1 - rn) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

Step-by-step explanation:

The sum of the first n terms of a geometric progression (GP) can be found using the formula:

1. Let Sn denote the sum of the first n terms of the GP.
2. The formula for Sn is given by: Sn = a * (1 - rn) / (1 - r), where a is the first term and r is the common ratio of the GP.
3. To find the sum of the series S1 + S2 + ... + Sn, we can use the formula for the sum of a finite geometric series: Sn = a * (1 - rn) / (1 - r).

Therefore, the sum of the series S1 + S2 + ... + Sn is Sn = a * (1 - rn) / (1 - r).