Question

Find the non-negative number of c.

Answer 1

\[f(n) = (1 - \frac{1}{2})(1 - \frac{1}{2^{2}})(1 - \frac{1}{2^{3}}) ... ((1 - \frac{1}{2^{n}})\]

Find and prove a non-negative number "c" such that f(n) > c for all n

Answer 2

c cannot be the largest c that will work, nor anywhere near it.

Answer 3

What do you mean by

c cannot be the largest c that will work, nor anywhere near it ?

If we compute the product like this:

http://www.wolframalpha.com/input/?i=product+from+1+to+infinity+of+%281-1%2F2^%28n%29%29

we see it "converges" to:

0.288788095086602421278899721929

so if we must choose a c value, it can be anywhere between 0 and 0.288788095086602421278899721929

Or am I misreading things?

Answer 4

The question was given that P(n) is always greater than 0.288. I am not really sure either