plz solve Po=[1+sum(n=1 to infinity)*product(i=0 to n-1)*a(i)/(b(i)+1)] raise to power -1?

Question

plz solve Po=[1+sum(n=1 to infinity)*product(i=0 to n-1)*a(i)/(b(i)+1)] raise to power -1 provided a/b<1
I hope all understood the question. the problem is to solve the summation of product.

Answer 1

If by a(i) and b(i) you mean "a times i" and "b times i", then:

For i = 0:

a*i / (b*i + 1) = 0 / 1 = 0

So you have:

Po = 1 / (1 + 0 + (0 * (a / (b + 1))) + (0 * (a / (b + 1)) * (2a / (2b + 1))) + ...)

Po = 1 / 1

Po = 1

If by a(i) and b(i) you mean a and b are infinite sequences (then presumably a / b means "for all i, a(i) / b(1) < 1"), well then that is something else entirely.

This reminds me of the problem to expand and simplify the product of twenty-six binomial terms:

(x - a) (x - b) (x - c) ... (x - z)

Answer 2

zero