If \(a + \frac{1}{b} = 1\;\) and \(b + \frac{1}{c} = 1\), then the value of \(c + \frac{1}{a}\) is –
If \(a + \frac{1}{b} = 1\;\) and \(b + \frac{1}{c} = 1\), then the value of \(c + \frac{1}{a}\) is –
1). 2
2). 1/2
3). 1
4). 0
1 answers
Given that,
$(a + \frac{1}{b} = 1)$
$( \Rightarrow a = 1 - \frac{1}{b})$
$(\Rightarrow \frac{1}{a} = \frac{b}{{b - 1}})$
and
$(b + \frac{1}{c} = 1\;)$
$(\Rightarrow \frac{1}{c} = 1 - b)$
$(\Rightarrow c = \frac{1}{{1 - b}})$
$(\therefore c + \frac{1}{a} = \frac{1}{{1 - b}} + \frac{b}{{b - 1}})$
$(\Rightarrow c + \frac{1}{a} = \frac{{b - 1}}{{b - 1}} = 1)$
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