Consider the infinite series defined by . What is the value of r from the ratio test? What does this r value tell you about the series? Consider the infinite series defined byn=12n!22n(a) What is the value of r from the ratio test?(b) What does this r value tell you about the series?

Ratio Test ⇒r=limn→∞an+1an⇒If r>1 then series divergent ⇒If r<1, then series convergent⇒If…

Answered: Consider the infinite series defined by…

Consider the infinite series defined by n=1 2n! 22n (a) What is the value of r from the ratio test? (b) What does this r value tell you about the series?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 55SE: The sum of an infinite geometric series is five times the value of the first term. What is the...

See similar textbooks

Related questions

Q: Consider the function y = f(x) graphed below. 1 Give the x-coordinate of a point where: A. the…

A: As per guideline we can solve 3 subparts only. please re-post the other parts and mention the parts…

Q: Compute the derivative of the following function. f(x) = 14xe5x f'(x) = 70xe5x + 14e5x

A: NOTE: Refresh your page if you can't see any equations. . take derivative use the product rule…

Q: Solve the initial value problem. ofy dt² y= - = 3 - e2t, y(1) = - 2, y'(1) = 2

Q: Angela and Brian have $1000 each and plan to put it into an account earning interest compounded…

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Given data: How do you use the method of cylindrical shells to find the volume, the x-axis (x=3+…

Q: dx Given the equation xy - y = 9y, find - by implicit differentiation. Answer dx dy ||

Q: The slope of the tangent line at any point on the graph of f(x) = 7x2 + 4x is given by the…

A: Given f( x ) = 7x2 + 4x f'( x ) = limh→0f( x + h ) - f( x )h

Q: A manufacturer's suggested retail price for a base model 2022 Ford Bronco is $36, 450 and, with…

A: According to bartleny guidelines we supposed to do the first three subparts of multiple subparts…

Q: Previous Problem List Next A conical water tank with vertex down has a radius of 14 feet at the top…

Q: Example 3: As a function, we have 1x1 = { = * -x for x < 0 for x ≥ 0 F(x) We will ALWAYS rewrite the…

A: Given : for x > 0 , |x|=x for x < 0 , |x|=-x for x = 0

Q: It is estimated that t days after a virus begins to spread in a town, the percent of the population…

Q: A. Graph the linear equation in two variables. Find at least five solutions in the table of values…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

Q: (3*10^(2))(2.3*10^(6)) Write your answer in scientific notation.

Q: Find the length of the following curve. x = (y/5)² -25 In (y/5), 2 ≤ y ≤ 10 The length of the curve…

Q: Evaluate the integral. (Use C for the constant of integration.) S + 6 dt

Q: joo 나 (X (1HX) dx

Q: Because of new patients, transplantations, and deaths, the number of patients recieving dialysis…

A: Given query is to find indicated limit.

Q: Use the table to below to answer questions for 19-27. -3 -2 -1 3 7 -1 0 -8 X f(x) 11 g(x) -8 9 -3 0…

Q: The equation of motion of a particle is s = t³ - 12t, where s is measured in meters and t is in…

Q: Suppose that f is given for x in the interval [0, 12] by 0 2 4 6 8 10 12 f(x)=-10-6-4-2-1-2-4 X = A.…

Q: cx + 8 163x if d Find values of c, d that make f(x) continuous at x = 1. Let f(x) = = с lim f(x) x-1…

Q: Find the average value of the function on the given interval. (Show work)

A: The objective is to find the average value of the function, f(x)=1+x2 on the interval -1,2. The…

Q: π/4 π/4 [*** (** 0 tan(x) sec²(y) dx dy

Q: An agent buys 200 items at a total cost of shs 600000. she sells 150 of them at loss of 8% . find…

A: An agent buys 200 items at a total cost of shs 600000. she sells 150 of them at loss of 8% .

Q: Consider the graph of the function f(x) shown below. A. f(12) ? f(15) 3. f(12) - f(9) ? ƒ(9) - f(6)…

A: Given query is to to find which is larger from the graph.

Q: Let f(t) = 3t - 7t². a) Find f(t + h): b) Find f(t+h)- f(t): f(t+h)-f(t) h c) Find d) Find f'(t):

Q: write the equation of a line tangent to (2x-1)(x-1) if the slope of the tangent is -11

A: Given: y=(2x-1)(x-1) slope =11

Q: The cost function, in dollars, of a company that manufactures food processors is given by C(x) = 200…

A: The cost function, in dollars, of a company that manufactures food processors is given by…

Q: Suppose f(x) = 4x² + 6x-3. Evaluate the limit by using algebra to simplify the difference quotient…

Q: Find the average value gave of the function g on the given interval. 5 1+t²' 9 ave = g(t) = [0, 7]

Q: Q2 Find an equation for the surface that contains all such points P that has equal distance to the…

Q: Find the volume generated by revolving the area bounded by the curve outside y=x^2 and between…

Q: Use implicit differentiation to determine Answer dx for the equation x + y² = 9. dy dx ||

A: Solution Given that equation is

Q: A bank features a savings account that has an annual percentage rate of r = 3.8% with interest…

Q: Differentiate. f'(x) = f(x) = ax + b cx + d

Q: The tangent line to y = f(x) at (1,—8) passes through the point (9,-7). Compute the following. a.)…

A: We can solve this as follows:

Q: Int dt

A: Given query is to find the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) 35 dx √x+xVx

Q: Now, write a piecewise function, state the transition points and tell the type of discontinuity at…

Q: Find the following limit or state that it does not exist. √36+h-6 h lim h-0 Simplify the given…

Q: (arcsinx)² dx

A: This is your answer

Q: Evaluate the integral. 64 S 64 log 4(x + 64) X + 64 dx log 4(x + 64) x + 64 (Type an exact answer.)…

A: Given query is to fins indicated integral.

Q: 8. Use the following: P(1, 3, 2), Q(2,0,−1), R(3, -1, 1) Find the normal vector and equation to the…

Q: 1. Find the average value of f(x,y) = 1 on the triangle with vertices (0,0), (1,0) and (1,2). If you…

A: Let's find average value of given function by double integral.

Q: f(x, y, z) = y² + z² and u = (1, 0, 1) at P(1,1,1).

A: To find the directional derivative of fx, y, z=y2+z2 at P1, 1, 1 in the direction of vector u=1, 0,…

Q: What is the limit of this infinite series? 5n5 (3 n=1 4n5 +5 Enter your answer in the box. Enter any…

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: NOTE: Refresh your page if you can't see any equations. . substitute .................put it…

Q: Use a graphing calculator to help you solve this equation: 2.1z² = 6.62 +6 Steps (if using TI 83 or…

Q: Now that we know derivative rules, we can leave behind the Limit Definition of the Derivative (but…

A: Here we have to find the equation of tangent line.

Question

Consider the infinite series defined by .

What is the value of r from the ratio test?
What does this r value tell you about the series?

Consider the infinite series defined by
n=1
2n!
22n
(a) What is the value of r from the ratio test?
(b) What does this r value tell you about the series?

Expert Solution

Step 1

$R a t i o T e s t \Rightarrow r = \lim_{n \to \infty} |\frac{a_{n + 1}}{a_{n}}| \Rightarrow I f r > 1 t h e n s e r i e s d i v e r g e n t \Rightarrow I f r < 1, t h e n s e r i e s c o n v e r g e n t \Rightarrow I f r = 1, t h e n r e s u l t i n c o n c l u s i v e$

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here