Prove the inequality:
\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2^{2}}\right)\ldots\left(1+\frac{1}{2^{n}}\right)<3.\)
How about:
.
Cannot prove it formally, but the LHS converges to 2.38423........., which is < 3
Can you prove that the LHS converges to 2.38423 ?
As I said "Cannot prove it formally", but it does converge to 2.38423..........
https://www.wolframalpha.com/input/?i=%E2%88%8F+%5B(1%2B2%5E-n),+n,+1,+1000%5D
∏ [(1+2^-n), n, 1, 1000] ≈2.384231029031371724149899288678397238772...............etc.
Thank you Alan.
+4609 
