Find 5 different demonstrations (proofs) of the Arithmetic Mean -- Geometric Mean inequality for two non-negative numbers
One example.
Another suggestion.
Some Algebra.
Another example.
And still another example . . .
More algebra . . .
Using some geometry . . .
Can you generalize this theorem?
In the case of three positive quantities:
In general,
For a discussion of one proof of these generalizations, see Courant,R.& Robbins, H. (1941) What is Mathematics? New York: Oxford University Press, pp. 361-365.
