Series and sequences

Find a fraction equivalent to the recurring decimal?

0.435643564356

Result

n =  44
d =  101

Solution:

a1=0.4356 q=0.0001 n=a1/(1q) k=10000 (1q)=10000 (10.0001)=9999 l=10000 a1=10000 0.4356=4356 s=l/k=4356/9999441010.4356 s=n/d=44/101 n=44a_{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=101d=101



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