JAMB - Mathematics (1978 - No. 5)
The sum of the progression is 1 + x + x2 + x3 + ......
\(\frac{1}{1 - x}\)
\(\frac{1}{1 + x}\)
\(\frac{1}{x - 1}\)
\(\frac{1}{x}\)
Explicació
Sum of n terms of Geometric progression is \(S_{n} = \frac{a(1 - r^n)}{1 - r}\)
In the given series, a (the first term) = 1 and r (the common ratio) = x.
\(S_{n} = \frac{1(1 - x^{n})}{1 - x}\)
a = 1, and as n tends to infinity
\(S_{n} = \frac{1}{1 - x}\)