First slide

Special Series in Sequences and Series

Question

If a, b, c are digits, then the rational number represented by 0.Cababab…… is

Moderate

A

$c a b l 990$
B

$(99 c + b a) 990$
C

$(99 c + 10 a + b) / 990$
D

${(a l d)}^{2}$

Solution

$L e t P = 0 . C a b a b a b$
$\begin{array}{l} \Rightarrow 10 P = c . a b a b a b \dots . \\ And 1000 P = c a b . a b a b a b \dots \end{array}$
Substracting Eq. (1) from Eq. (2). We have 990 P = cab –c
$Or P = \frac{100 c + 10 a + b - c}{990} = \frac{99 c + 10 a + b}{990}$

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