For 8b.
You've shown it's true for
S2, and looks like you've going for induction.
For your induction step, it's not clear whether you know what you're summing as you've put nothing under the summation signs, and what you have put doesn't look right.
I suggest writing out
SN+1 and
SN, subtract the latter from the former and see what you get. You should have three terms left.
Hint: You want to show it's >0.