Let H be an inner product space. Suppose is a sequence in H and g is a vector in H.

I know how to do (a), which is to show that converges to 0 as n goes to infinite.

I need help on part (b).

a. Show that if || fn || || 9 || and (fn,g) + (9,9) as n +00, then fn +9 as n +0. b. Must the conclusion of part (a) be true if the hypothesis that (frog) 19,9) is omitted? Justify your answer. a. Show that if || fn || || 9 || and (fn,g) + (9,9) as n +00, then fn +9 as n +0. b. Must the conclusion of part (a) be true if the hypothesis that (frog) 19,9) is omitted? Justify your