prove or give a counter example is sum ai and sum bi are convergent series with non-n

math25

the Cauchy-Schwarz inequality:

sum ai bi is less then or equal to sum (ai^2)^1/2 sum (bi^2)^1/2

math25	the Cauchy-Schwarz inequality: sum ai bi is less then or equal to sum (ai^2)^1/2 sum (bi^2)^1/2