2 Hints

As per usual, here’s where you’ll find the problem sheet hints!

1. Think about all the methods you know for proving whether a series converges. Some of the methods from the tutorial may come in handy…
2. Pretty much the same as homework question 1. However, for part…
   2. I’ve got a few pointers for this one. Make sure you know how the binomial coefficient is defined. Also, try to avoid expanding any unnecessary brackets — if you’re writing \(n^3, n^4\) etc. in your solutions, you’re putting in more effort than needed!
3. This one is only slightly more involved. Know your definitions, and again, think of possible convergence tests to apply.
4. 1. For this part, use the convergence definition with a specific \(\epsilon\) alongside the pinching theorem.
   2. Use part i) — for reference, this is a special case of what is known as the root test for series.
5. This is similar to Tutorial Question 4.