Let a+ar1+ar12+⋯+∞ and a+ar2+ar22+⋯+∞ be two infinite series of positive numbers with the same first term. The sum of the first series is r1 and the sum of the second series is r2. Then the value of (r1 + r2) is ______.

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answer is 1.

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Detailed Solution

a1−r1=r1 and a1−r2=r2Hence, r1 and r2 are the roots of a1−r=r⇒ r2−r+a=0⇒ r1+r2=1

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