Question

Find the sum of the GP : 

1 – a + a² – a³ + …to n terms ( a ≠ 1)

Answer 1

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

n terms

\(\therefore\) S_n = 1 \(\times\) \(\frac{(-a)^n -1}{-a-1}\)

[Multiplying both numerator and denominator by -1]

\(\Rightarrow\)  S_n = \(\frac{1-(-a)^n}{1+a}\)