Question

How do you do this question?

Answer 1

Problem 1

You are correct. The answer is choice C.

A sequence is just a list of numbers where the order matters. Something like (1,2,3,4,5) is different from (3,1,2,5,4)

A series is where you add up that list of numbers to get a single value. For instance, the sum of the list (1,2,3) is 1+2+3 = 6. This is basically a partial sum when talking about infinite sequences because the next partial sum would be 1+2+3+4 = 10 and the next partial sum would be 1+2+3+4+5 = 15, and so on.

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Problem 2

Answer: Choice A

Why is this? Each time we get a partial sum, we're basically forming a new sequence. We're forming a sequence of sums. Going back to the example in problem 1, we had the partial sums (6,10,15). If we keep this process going, we'll have the list of partial sums grow forever and not approach some finite value. Therefore, this series diverges.

If the sums were to slowly get closer to some fixed value, then we would say the series converges.