Inspired by Sai Ram

Algebra Level 4

The sum of the sequence \( 0.1 , 0.11 , 0.111 , 0.1111 , \ldots \) upto \(n\) terms is given by \( \large \frac{e}{a} ( n-\frac{1}{b}(1-(\frac{1}{c})^{dn} )) \) for positive integers \(a,b,c,d\) and \(e\) with \(\gcd(a,e) = 1 \).

Find the value of \(a+b+c+d+e\).

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