​ Find the sum of the GP : 1 - 1/3 + 1/3^2 - 1/3^3 + ..... to n terms ​

Question

Find the sum of the GP :

1 - \(\frac{1}{3}\) + \(\frac{1}{3^2}\) - \(\frac{1}{3^3}\) + ..... to n terms

Answer 1

Sum of a G.P. series is represented by the formula, s_n = a\(\frac{1-r^n}{1-r}\), when |r|<1. 

‘S_n’ represents the sum of the G.P. series up to n^th terms, 

‘a’ represents the first term, 

‘r’ represents the common ratio and 

‘n’ represents the number of terms. 

Here, 

a = 1

r = (ratio between the n term and n-1 term) -\(\frac{1}{3} \div 1 = -\frac{1}{3}\)

n terms