For what values of r is the sequence {rn} convergent?
we know that limx โ [infinity] ax...
Mathematics, 26.11.2019 01:31 EmmaKozlewski4907
For what values of r is the sequence {rn} convergent?
we know that limx โ [infinity] ax = [infinity] for a > 1 and limx โ [infinity] ax = 0 for 0 < a < 1. therefore, putting a = r and usingthis theorem, we have
lim n โ [infinity] rn = [infinity] if r > 1 ,
lim n โ [infinity] r^n = if 0 < r < 1.
it is obvious that
lim n โ [infinity] 1n = and lim n โ [infinity] 0n = .
if โ1 < r < 0, then < |r| < , so
lim n โ [infinity] |rn| = lim n โ [infinity] |r|n =
and therefore limn โ [infinity] rn = by this theorem. if r โค โ1, then {rn} diverges as in this example. the figures show the graphs for various values of r.
Answers: 1
Mathematics, 21.06.2019 16:40
Which of the following is the correct equation for this function? a. y= (x+4)(x+2) b. y=x^2+ 3x โ 2 c. y+ 2 = โ 2(x+3)^2 d. y+ 2 = 2(x+3)^2
Answers: 1
Mathematics, 22.06.2019 00:30
Simplify the given expression leaving the answer in improper fraction form. 2/3+5/6
Answers: 2
Mathematics, 05.05.2020 07:52
English, 05.05.2020 07:52
Biology, 05.05.2020 07:52
Health, 05.05.2020 07:52
History, 05.05.2020 07:52
Mathematics, 05.05.2020 07:52
Mathematics, 05.05.2020 07:52
English, 05.05.2020 07:52
Social Studies, 05.05.2020 07:52