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If the sum of the infinite geometric series a b + a b^2 + a b^3 + . is 4 , then find the sum of a (a+b) + a (a+b)^2 + a (a+b)^3 + = p q where p and q are co-prime, then find the value of (p+q) .

Correct answer

9

Step-by-step solution

Given ( a b ) ( b-1 b ) =4 a=4(b-1) ...(1) To find S= ( a a+b ) (1- 1 a+b ) = a a+b-1 ...(2) From Eqns. (1) and (2) S= 4 5

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