Let 'X' denotes the value of the product...

Let 'X' denotes the value of the product.`(1+a+a^2+a^3+.........oo)(1+b+b^2+b^3+.............oo)` where `a` and `b` are the roots of the quadratic equation `11x^2-4x-2=0` and `Y` denotes the numerical value of the infinite series. `(log_b 2)^0 (log_b 5^4^0)+(log_2) (log_b,5^4^2)+............oo` where `b =2000`. Find `(XY).`

`1/5`

`13/6`

`11/15`

`22/35`

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