Find the sum of the GP : 1 – a + a2 – a3 + …to n terms ( a ≠

1.	Find the sum of the GP : 1 – a + a2 – a3 + …to n terms ( a ≠ 1)
Answer» 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 = \(\frac{1-(-a)^n}{1+a}\)

Find the sum of the GP : 1 – a + a2 – a3 + …to n terms ( a ≠ 1)

Answer»

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