Lecture 3 - Sequence of Partial Sums, Geometric & Harmonic Series

Question 1

{a(sub n)} is increasing if:

Answer 1

Question 2

{a(sub n)} is nondecreasing if:

Answer 2

Question 3

{a(sub n)} is decreasing if:

Answer 3

Question 4

{a(sub n)} is nonincreasing if:

Answer 4

Question 5

{a(sub n)} is monotonic if:

Answer 5

Question 6

If {a(sub n)} is bounded above and below then we say that {a(sub n)} is a what?

Answer 6

Bounded sequence

Question 7

What is the convergence of a bounded monotonic seuqnce?

Answer 7

It converges

Question 8

What is an infinite series?

Answer 8

Question 9

What is a sequence of partial sums?

Answer 9

Question 10

If the sequence of partial sums {S(sub n)} has a limit L, the infinite series does what?

Answer 10

It converges to that limit.

Question 11

If the sequence of partial sums diverges, then the infinite series does what?

Answer 11

It also diverges

Question 12

Suppose the series a(sub k) converges to A and c is a real number. Does the series ca(sub k) converge? If so, to what?

Answer 12

It converges to cA (you can take the constant out of the series initially and multiply it back at the end)