This can also be written as
= \(\big( {\text{x}^2} + \frac{1}{{\text{x}^2}} + 2\big)\) + \(\big( {\text{x}^4} + \frac{1}{{\text{x}^4}} + 2\big)\) + \(\big( {\text{x}^6} + \frac{1}{{\text{x}^6}} + 2\big)\) + ....... to n term
Sum of a G.P. series is represented by the formula, Sn = a\(\frac{r^n - 1}{r-1}\), when r≠1.
‘Sn’ represents the sum of the G.P. series up to nth terms,
‘a’ represents the first term,
‘r’ represents the common ratio and
‘n’ represents the number of terms.
a = X2, \(\frac{1}{{\text{x}} ^2}\)
r = (ratio between the n term and n-1 term) X2, \(\frac{1}{{\text{x}} ^2}\)
n terms
(ii) If we divide and multiply the terms by (x-y)
Sum of a G.P. series is represented by the formula, Sn = \(a\frac{r^n - 1}{r-1}\), when r≠1.
‘Sn’ represents the sum of the G.P. series up to nth terms,
‘a’ represents the first term,
‘r’ represents the common ratio and
‘n’ represents the number of terms.
Here,
a = x2 , y2
r = (ratio between the n term and n-1 term) x, y
n terms