Let's break it down into some steps. First consider the problem for a moment;
We have the series U(n+1) = U(n)^2, U(1) = 0.5
By hand we can tell that the next few terms in the series are; U(2) = .5*.5 = 0.25, U(3) = .25*.25 = 0.0625, U(4) ~= 0.0039, ...
Here's a question for you: How can we get these numerically? Can you give me a for-loop that computes each of these?
Now, the next condition is deciding when to stop. Since we are computing the sum, we are going to stop when we end up adding very small terms. Hence we'll get an approximate answer. We've decided that this will be when U(n) < 10^(-8). Perhaps we can check this condition with an if or a while statement? Can you give an example of one of these?
If you can implement these two parts, I think you will see the answer.
