Let `a+a r_1+a r1 2++ooa n da+a r_2+a r2 2++oo` be two infinite series of positive numbers with the same first term. The sum of the first series is `r_1` and the sum of the second series `r_2dot` Then the value of `(r_1+r_2)` is ________.

Answer

4

Explanation

`a/(1-r_(1))=r_(1)` and `a/(1-r_(2))=r_(2)`
Hence, `r_(1) and r_(2)` are the roots of `a/(1-r)=r`
`rArrr^(2)-r+a=0`
`rArrr_(1)+r_(2)=1`