Question: Suppose that a n and b n are series with positive an n b n terms. Prove that if and b n

Suppose that Σ an and Σ bn are series with positive an n→∞ b n terms. Prove that if an lim n0 b n. = 0 and Σ bn converges, Σ an also converges.

an lim n0 b n. = 0

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

an Suppose lim n bn 0 and Eb converge... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 10th Edition Questions!

Q:

Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? (b) If an

Q:

Prove that if (an is convergent series of positive terms then (In (1 + an) converges?

Q:

Let be a random process, where An and Bn are random variables such that , E[An]= E[Bn]= 0 E[AnBm] = 0 E[AnAm] dn, mE An = [ 2] E[BnBm] δn, mE [ Bn 2], , and for all and , where is the...

Q:

Use the result of Exercise 59 to show that each series converges. (a) (b) Data from in Exercise 59 Suppose that a n and b n are series with positive an n b n terms. Prove that if and b n...

Q:

3. [8 points] Let a1, a2, a3, ... be a sequence of positive numbers such that the power series Can (2 + 1 ) " 7 = 0 has a radius of convergence R = NICT (a) On what (open) interval does the series >...

Q:

answer please DIRECT COMPARISON TEST is presented in $5.4 of the OpenStax text. DIRECT COMPARISON TEST: Let \\ a, and \\ b,, be infinite series with positive terms. n=1 Suppose we know the behavior...

Q:

Test the series for convergence or divergence. 8 10 IN + + 9 10 Identify b . (Assume the series starts at n = 1.) Evaluate the following limit. lim D Since lim b ?| 0 and by + 1 ? vb for all n,...

Q:

Please help with the following questions: The Comparison Test. ac 5X3 Suppose that Z a\" and Z 3)" are series with positive terms, and an 3 bn for all n (or for \".0. large). n21 n21 IX; (X) o If E...

Q:

(Review) Consider the integral f VET dx. Which of the following trigonometric substitutions should be used to evaluate this integral? a. x = cos 0 b. x = sin 0 C. x = tan 0 d. x = sec 0 e. None of...

Q:

4. (a) Suppose that an and n=1 n=1 (b) Use part (a) to show that an Show that, if bn converges, then an also converges. (Hint: For sufficiently large n, n=1 n=2 bn are series of nonnegative terms...

Q:

Consider a configuration of n identical units, each consisting of three layers. The first layer is a column of 3-1 1 air of height h = = cm, and the second and third layers are of equal thickness d =...

Q:

The pipe assembly is secured on the wall by the two brackets. If the flower pot has a weight of 50 lb, determine the magnitude of the moment produced by the weight about the OAaxis. 4 ft 3'ft 4 ft 60...

Q:

Cullumber manufacturing purchased machine on Jan 1 2 0 2 3 for use in its factory. It paid $ 7 3 4 , 0 0 0 or the machine and estimated that it had a useful life of 1 0 years. at the end of which the...

Q:

_____________functions are usually related to esteem appearance. (a) Primary (b) Secondary (c) Tertiary (d) None of the above AppendixLO1

Q:

In problem, find the exact value of each logarithm without using a calculator. log 5 25

Q:

9% compounded quarterly or 9%compounded annually In problem, determine the rate that represents the better deal.

Q:

In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential,...

Q:

c. based ca the busis. c. based ca the basis. 15. You have purchased a duplex property for \$275,000. The property's assessed value nas allocated ta: a land and mprevements c. buidings and animals c....

Q:

Pappy's Potato has come up with a new product, the Potato Pet ( they are freeze - dried to last longer ) . Pappy's paid $ 1 6 0 , 0 0 0 for a marketing survey to determine the viability of the...

Q:

Williamson Industries has $3 billion in sales and $2.385 billion in fixed assets. Currently, the company's fixed assets are operating at 90% of capacity. a. What level of sales could Williamson...