I need a correct answer please 4 20 pts 1 For any given a b

I need a correct answer please

4. (20 pts) (1) For any given a, b 2 0, show that Vas (2) Suppose that both a1 and b are convergent. Show that a,b, converges absolutely. (3) Suppose a, converges. Show that a, a +b , show that Vab

Solution

1.)  (a - b)^2 0
=> (a + b)^2 - 4ab 0
=> (a + b)^2 4ab
=> (a + b) 2(ab)
=> 2(ab) (a + b)
=> (ab) (a + b)/2.

2.) As aj^2 and bj^2 converges,

So, aj bj will also converge absolutely

So, their product will also converge absolutely.

3.) Same reason.