Show that if and are convergent then is absolutely convergent.
Hint: Show |xy| <= 1/2(|x|^2 + |y|^2) for any x,y ε R
I can prove the Hint -
And this is true for all x, y as the square of any real number will be greater than or equal to 0.
But I cant see how to apply this to the original question?
Thank you for the help guys.
There is one thing I am still not sure about - what is the meaning of ?
Does that mean that the series is made up by squaring each term and adding them together - a0a0 + a1a1 + a2a2 + ... + anan?
Or does it mean that the series you get the sum of series and then square it?