6th Problem

Algebra Level 3

If the sum of the infinite geometric series ab+ab2+ab3+\frac{a}{b}+\frac{a}{b^{2}}+\frac{a}{b^{3}}+\ldots is 4, then what is the sum of a(a+b)+a(a+b)2+a(a+b)3+?\frac{a}{(a+b)}+\frac{a}{(a+b)^{2}} +\frac{a}{(a+b)^{3}}+\ldots ?

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