# Series and sequences

Find a fraction equivalent to the recurring decimal?

0.435643564356

Result

n =  44
d =  101

#### Solution:

$a_{1}=0.4356 \ \\ q=0.0001 \ \\ n=a_{1}/(1-q) \ \\ k=10000 \cdot \ (1-q)=10000 \cdot \ (1-0.0001)=9999 \ \\ l=10000 \cdot \ a_{1}=10000 \cdot \ 0.4356=4356 \ \\ s=l/k=4356/9999 \doteq \dfrac{ 44 }{ 101 } \doteq 0.4356 \ \\ s=n/d=44/101 \ \\ n=44$
$d=101$

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