Question

Find the sum to infinity in each of the following Geometric Progression.

(i) 1, \(\frac{1}{2}, \frac{1}{2^2}\frac{1}{2^3}\)........

(ii) 5, \(\frac{20}{7}, \frac{80}{49}\),........

Answer 1

(i) S_∞ = 1 + \(\frac{1}{2} + \frac{1}{2^2} + \frac{1}{3^2}\), .........

= \(\frac{1}{1-\frac{1}{2}} = 2\)

(ii) S_∞ = 5 + \(\frac{20}{7} + \frac{80}{49} + \)......

= \(\frac{5}{1-\frac{4}{7}} = \frac{35}{3}\)