10.2

Question 1

What is the general form of a geometric series

Answer 1

The summation from 1 to infinity of ar^(n-1)

Question 2

How do you determine the convergence of a geometric series?

Answer 2

If -1<r<1 then the series converges to a/(1-r) where a is the first term. If |r|>=1, the series diverges

Question 3

What does the nth term test say

Answer 3

A series from 1 to infinity of an diverges if the limit as n approaches infinity of an fails to exist or is different from zero. This does not mean that all series with limit 0 converge.

Question 4

∑(an+bn)

Answer 4

A+B

Question 5

∑(an−bn)

Answer 5

A-B

Question 6

∑kan

Answer 6

kA

Question 7

If ∑an converges and ∑bn diverges, what can be said about ∑(an+bn) and ∑(an-bn)

Answer 7

Both diverge. This is not necessarily the case if both diverge, only if one does.

Question 8

How do you raise the starting value of n of a summation?

Answer 8

Replace the starting point of the summation with (1+h), and the value of n in the summation with (n-h)

Question 9

How do you lower the starting value of n in a summation?

Answer 9

Replace the starting point with (1-h), and the value of n in the formula with (n+h)

Question 10

What is the sum of an alternating geometric series with |r|<1?

Answer 10

a/(1+r)