Let an = (1+1/3) * (1+1/5) * (1+1+7+* * [1+655].

bn =( 1+ 1/4)*( 1+ 1/6)*( 1+ 1/8)+*……*[ 1+ 1/(2n)]。

Obviously an> 10 billion

an=(4/3)*(6/5)*(8/7)*...*[2n/(2n- 1)]；

bn=(5/4)*(7/6)*(9/8)*...*[(2n+ 1)/(2n)]。

And (an) 2 > an * bn = (2n+1)/3 > (2n+1)/4.

Therefore, an (1+1/3) * (1+1/5) * (1+1/7) * * [1+]

Method 2,/z/q//z/q 148942658.htm

Proof 3,/Neirong-Shenmo-Dui-Wangshan-Shenmo-Jingyan-Ziliao-No-Ziliao-. Hypertext markup language

Commonly used in college entrance examination:

Comparison method: compare the sizes of two formulas and find the difference or quotient. It is the most basic and commonly used method.

Synthesis method: When applying the knowledge of mean inequality, we must pay attention to when the equal sign is established.

Analytical method: When we can't start with the conditions, we should think by analytical method, but we should still prove by comprehensive method. These two methods are inseparable.

Method of substitution: Imagine inequality as a trigonometric function, which is convenient for thinking.

Reduction to absurdity: the hypothesis is not established, but it cannot be solved, so it is established.

Scaling method:

Proved by Cauchy inequality. etc ......

It's best not to use extra-curricular inequality: if you use it wrong, the teacher can't understand it. Just type it wrong and use it if you can.

Extracurricular inequality:

This is a lot.

I'll call the tenth.

Cauchy inequality (this is extra-curricular, because there are few elective parts)

Jacob Starr inequality

AG inequality

Holder inequality

Hooke inequality

Cobb inequality

Carlson inequality

Recursive inequality

Sequential inequality

Triangle inequality

Zhan Sen inequality

Hidden, but I still hope to adopt extra points. O(∩_∩)O Thank you.