A(x)=x+x+x+⋱111
With A(x) defined as above, where the continued fraction goes on indefinitely, find the value of the infinite product
A(1)1×A(1)1+11×A(1)1+1+111×⋯.
If your answer can be expressed as cba+b, where a,b,c are positive integers and b is square-free, give your answer as 100a+10b+c.
Bonus: Can you give a closed formula for A(y)y×A(y)y+y1×A(y)y+y+y11×⋯ when it converges?
Your answer seems reasonable.
Find out if you're right!