# 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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