Mathematics, 25.10.2020 07:10 ashquinn

How do you do this question?

Answers

Answer from: Boris1002

k > 1, or k ≥ 2

Step-by-step explanation:

aₙ = (n!)² / (kn)!

aₙ₊₁ = ((n+1)!)² / (k(n+1))!

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[((n+1)!)² / (k(n+1))!] / [(n!)² / (kn)!]│

lim(n→∞)│[((n+1)!)² / (k(n+1))!] × [(kn)! / (n!)²]│

lim(n→∞)│[((n+1)!)² / (n!)²] × [(kn)! / (k(n+1))!]│

lim(n→∞)│[((n+1)! / n!)²] × [(kn)! / (kn+k)!]│

lim(n→∞) (n+1)² × (kn)! / (kn+k)!

This converges when the limit is less than 1.

If k=1:

lim(n→∞) (n+1)² × n! / (n+1)! = lim(n→∞) (n+1) = ∞

If k=2:

lim(n→∞) (n+1)² × (2n)! / (2n+2)! = lim(n→∞) (n+1)² / [(2n+2)(2n+1)] = 1/4

If k=3:

lim(n→∞) (n+1)² × (3n)! / (3n+3)! = lim(n→∞) (n+1)² / [(3n+3)(3n+2)(3n+1)] = 0

The series converges for k > 1, or k ≥ 2.

Answer from: Quest

i dont know

step-by-step explanation:

Answer from: Quest

What mathematical statement is missing ? ? the answer is b

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, kissesforlester7097

Given right triangle xyz, which correctly describes the locations of the sides in relation to

Answers: 1

continue

Mathematics, 21.06.2019 19:00, L3Zenith

What is not true about kl and mn? what is mn? (show )

Answers: 2

continue

Mathematics, 21.06.2019 21:30, fheight01

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.

Answers: 3

continue

Mathematics, 21.06.2019 21:40, jasmine8142002