what is cauchy schwarz inequality?? explain with example..

For all real numbers a1, a2, a3, a4.....an and b1, b2, b3, b4 and so on till bn
(a1^2 +a2^2+a3^2......)(b1^2+ b2^2+.....bn^2)>= (a1b1)^2+(a2b2)^2+......(anbn)^2

CAN U PLEASE EXPLAIN WITH AN EXAMPLE??

Take 3 real numbers 1,2,3 in one set and -1,-2,-3 in another set,
(a1^2 +a2^2+a3^2......) = 1+4+9 = 14
(b1^2+ b2^2+.....bn^2) = 1+4+9 = 14
Now (a1b1)^2+(a2b2)^2+......(anbn)^2 = (1*-1)^2 + (2*-2)^2 + (3*-3)^2 = 98
Now 14*14> 98