+0

# prove the inequality

0
62
5
+1167

Prove the inequality:

$$\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2^{2}}\right)\ldots\left(1+\frac{1}{2^{n}}\right)<3.$$

tertre  Oct 17, 2017

#4
+26328
+2

.

Alan  Oct 19, 2017
Sort:

#1
0

Cannot prove it formally, but the LHS converges to 2.38423........., which is < 3

Guest Oct 18, 2017
#2
+91007
0

Can you prove that the LHS converges to 2.38423 ?

Melody  Oct 19, 2017
#3
0

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.

Guest Oct 19, 2017
#4
+26328
+2

.

Alan  Oct 19, 2017
#5
0

Thank you Alan.

Guest Oct 19, 2017

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details