## Question

###### How do you find the interval of convergence #Sigma x^(2n)/(n*5^n)# from #n=[1,oo)#?

How do you find the interval of convergence #Sigma x^(2n)/(n*5^n)# from #n=[1,oo)#?

## Answers

#-sqrt5lt=xltsqrt5# ## Explanation:

Find the ratio

#abs(a_(n+1)/a_n)# for the series#suma_n# :

#abs(a_(n+1)/a_n)=abs(x^(2(n+1))/((n+1)5^(n+1))((n(5^n))/x^(2n)))=abs(x^2/5(n/(n+1)))# The series converges if

#lim_(nrarroo)abs(a_(n+1)/a_n)<1# .

#lim_(nrarroo)abs(a_(n+1)/a_n)=lim_(nrarroo)abs(x^2/5(n/(n+1)))=x^2/5lim_(nrarroo)abs(n/(n+1))=x^2/5# So the series is convergent for

#x^2/5<1#

#x^2-5<0#

#(x-sqrt5)(x+sqrt5)<0#

#-sqrt5 < x < sqrt5# Test both these endpoints by plugging them into the original series expression. Note that

#x=sqrt5# gives the divergent series#sum_(n=1)^oo 1/n# , whereas#x=-sqrt5# gives the conditionallyconvergentseries#sum_(n=1)^oo(-1)^n/n# . Thus,#x=-sqrt5# is included in the interval:

#-sqrt5lt=xltsqrt5#

#### Similar Solved Questions

1 answers

##### How do you determine the intervals for which the function is increasing or decreasing given #f(x)=abs(x^2-4)#?

How do you determine the intervals for which the function is increasing or decreasing given #f(x)=abs(x^2-4)#?...

1 answers

##### Help!!! Don't understand anything Read the following Consultation Report and answer the questions that follow. (l2pe)...

Help!!! Don't understand anything Read the following Consultation Report and answer the questions that follow. (l2pe) Consultation Note Day, Phyllis 5/25/x Med Record: P25882 HISTORY OF PRESENT ILLNESS: This 66-year-old former blackjack dealer is under evaluation for hyperparathyroidism. Su...

1 answers

##### Active Learning Template - Nursing Skills Chest Tube Insertion and Monitoring: Care for Client's Chest Drainage...

Active Learning Template - Nursing Skills Chest Tube Insertion and Monitoring: Care for Client's Chest Drainage System Chapter 18 in the ATI med surg book. description of skill Indications Nursing Interventions outcomes/evaluation client education potiential complications nursing interv...

1 answers

##### A normal good is which of the following? A good in which the change in price...

A normal good is which of the following? A good in which the change in price is proportionately related to a change in demand. A good in which a change in income is inversely related to the change in demand. A good in which a change in price is inversely related to a change in demand. A good in whic...

1 answers

##### Determine the value of x such as its matrix its equal to its inverse?

the matrix values are: upper left: 3 upper right: x lower left: -2 lower right: -3...

1 answers

##### 1. loe melts at 0C with an enthalpy of fusion -6.01 kJ mol". An ice cube...

1. loe melts at 0C with an enthalpy of fusion -6.01 kJ mol". An ice cube with a mass of 20.0g is placed inside an incubator at 40.0C°. Determine the total entropy change (in J/K) of this system....

1 answers

##### *Please use StdIn. not Scanner. Thanks Write a program that reads in lines from standard input...

*Please use StdIn. not Scanner. Thanks Write a program that reads in lines from standard input with each line containing a name and two integers and then prints a table with a column of the names, the integers, and the result of dividing the first by the second, accurate to three decimal places. You...

1 answers

##### -0. (incorrect) 8. (1 point) Compute the following limits using l'Hôpital's rule if appropriate. Use INF...

-0. (incorrect) 8. (1 point) Compute the following limits using l'Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote 1 - cos(8x) lim x+01 – cos(7x) 8x – 7* – 1 lim x² - 1 Answer(s) submitted: toy (incorrect) 9. (1 point) Compute the following ...

1 answers

##### How do you find the domain and range of #f(x) = x^3 - 3x + 2#?

How do you find the domain and range of #f(x) = x^3 - 3x + 2#?...

1 answers

##### How do you convert (15, -3) into polar coordinates?

How do you convert (15, -3) into polar coordinates?...

1 answers

##### What is output? public abstract class People { protected string name; protected int age; public abstract...

What is output? public abstract class People { protected string name; protected int age; public abstract void PrintInfo(); public void PrintInformation() { System.out.println("In Base Class People"); public class Teacher extends People { private int experience; public void PrintInfo() { Syst...

1 answers

##### 12) Isabella owns all 100 shares of Finch Corporation's stock, valued at $100,000. Abigail owns property...

12) Isabella owns all 100 shares of Finch Corporation's stock, valued at $100,000. Abigail owns property that has a $15,000 adjusted basis and a $100,000 FMV. Abigail contributes the property to Finch Corporation in exchange for 100 shares of newly issued Finch stock. Does Sec. 351 apply to Abig...

1 answers

##### Some measurements of the initial rate O KINETICS AND EQUILIBRIUM Deducing a rate law from initial...

some measurements of the initial rate O KINETICS AND EQUILIBRIUM Deducing a rate law from initial reaction rate data Some measurements of the initial rate of a certain reaction are given in the table below H2 initial rate of reaction 1.96 MI 0.945 MI 1.96 M 2.67 M 3.42 MI 0945 MI 37.0 M/s 295. M...

1 answers

##### What type of protein in cAMP signal transduction would be analogous to the phosphatases of phosphorylation...

What type of protein in cAMP signal transduction would be analogous to the phosphatases of phosphorylation cascades?...

1 answers

##### 11. Given the matrices A, B, and C shown below, find (A+B)C. = li 3 2...

11. Given the matrices A, B, and C shown below, find (A+B)C. = li 3 2 - 5], B = [4 / 1.0 -2 3 23.c = LA 11 2 3. -2...

1 answers

##### In 1993, Splish Company completed the construction of a building at a cost of $2,480,000 and...

In 1993, Splish Company completed the construction of a building at a cost of $2,480,000 and first occupied it in January 1994. It was estimated that the building will have a useful life of 40 years and a salvage value of $75,200 at the end of that time. Early in 2004, an addition to the building wa...

1 answers

##### Cornwell Products has adopted an ABC costing system to allocate its overhead costs. The following manufacturing...

Cornwell Products has adopted an ABC costing system to allocate its overhead costs. The following manufacturing activities and cost drivers have been identified: Activity Machine setup Machining Polishing Quality control Facility-level costs Total overhead costs Estimated OH Costs $180,000 $1,050,00...