1AM = Arithmetic mean
GM = Geometric mean
The inequality is AM ≥ GM with equality existing only if all terms are equal.Remember it exists only for be non negative.
Lets take two numbers first 'a' and 'b'
Therefore AM ≥ GM yields a+b2 ≥ √ab
Proof
squaring both sides we get (a+b)2 ≥ 4ab
(a-b) 2 ≥ 0 which is always true hence AM ≥ GM
Generalization x1 + x2+x3+... + xnn ≥ [nrt]x1x2x3...xn
There are many applications of this inequality and many tough problems can be easily solved using it .
Like a + 1a ≥ 2 where a is any positive real number
ab + bc + cd +da ≥ 4 where a,b,c,d are positive real number
I guess you are very interested in pure maths .. Keep up the good work :)
