Problem 6. ( 20 points) In this problem, we will show that the following inequality holds for all n : i=1ni212 Using induction to show this is quite tricky. We will introduce an even stronger statement that is easier to work with. This is a very common trick in mathematics, as sometimes stronger statements are easier to prove than the original statement. i=1ni212n1 Use induction to prove this inequality. In your inductive step, you may freely use the following inequality as a known fact: n+11n1+(n+1)210n0 Additional note: In this problem, we showed that the sum converges as it is always bounded by a constant (in other words, this sum is O(1) ). Interestingly, i=11/i2=2/6