Question: Show that if n=1 a n converges, then converges. 8 n=1 (an)) 1+ sin (an) 2

Show that if ∑∞n=1an converges, then8 n=1 (an))" 1+ sin (an) 2


converges.

8 n=1 (an))" 1+ sin (an) 2

Step by Step Solution

★★★★★

3.39 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

answer Since n1an converges we know that an 0 as n Now note th... 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 Precalculus Questions!

Q:

Prove that if And Both converge then Converges absolutely. First show that 2|akbk| ( a2k + b2k? bk 2/ az

Q:

Show that if n > 2, then Use this inequality to prove that e is not a rational number. 2! n+ 1

Q:

Show that if n | m, where n and m are integers greater than 1, and if a b (mod m), where a and b are integers, then a b (mod n)?

Q:

Instructions: Each question will be graded both for correctness and for work shown. The latter is extremely important solutions should be written using proper English (that means, appropriate grammar...

Q:

1. (8 points) Sections 5.1-5.2 a. Show that the sequence 97 n! converges. b. Show that the series (-1)" converges. n 2. (16 points) Sections 5.4 5.5 Determine the appropriate Taylor series expansion...

Q:

The integral function ( n ) = 0 t n - 1 e - t d t is defined for all real numbers n such that n 1 ( a ) Show that the integral defining ( n ) converges whenever n 1 . ( Hint: Explain why there exists...

Q:

diverges or converges QUESTION 24 Which statement is true, concerning the series? (1) n+1 (2) n= 3n2 - 1 iM 8 2" + 1 3- 22n - 1 Of (1) diverges, (2) converges O B Both converge or (1) converges...

Q:

Solve number 1 on the attached pdf I am trying to find An, A16 and the part with the symbol, like a E with 16 on top, n=1 on the bottom and An in front plus is it convergent or divergent. The series...

Q:

The gamma function, which plays an important role in advanced applications, is defined for n 1 by (a) Show that the integral defining (n) converges for n 1 (it actually converges for all n > 0)....

Q:

10\" (2n)! converges to a real number. [5] 5. (a) Show that 2 n=1 1 n [3] (b) What is the value of lim 0 . (Hint. Use part (a) of the question). nmo (2n)

Q:

What are two ways in which estimating uncollectible accounts improves the accuracy of the financial statements?

Q:

In the year just ended, Callaway Lighting had sales of $5,000,000 and incurred a cost of goods sold equal to $4,500,000. The firms operating expenses were $130,000 and its increase in retained...

Q:

Ch 1 0 ROI & Residual Income i \ table [ [ Joel de Paris, Incor, \ table [ [ Sheet ] , [ Beginning ] , [ Balance ] ] , Ending Balance ] , [ Assets ] , [ Cash , $ 1 4 0 , 0 0 0 , $ 1 2 0 , 0 0 0 ] , [...

Q:

An experiment was performed to investigate whether there is deterioration in the performance of a car if it uses unleaded fuel rather than leaded fuel. Ten cars filled with leaded fuel were run on...

Q:

A model for the surface area of a human body is given by S = 0.1091w0.425h0.725, where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. If the errors in...

Q:

In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as B(m, h) = m/h 2 , where m is the mass in kilograms and h is the height in meters. (a) What is the linear...

Q:

Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 3). You dont have an equation for S but you know that the curves both lie on S. Find an equation of the...

Q:

What costs would a firm following a flexible current asset management strategy consider, and why?

Q:

If the times interest ratio: A. Increases, then risk increases B. Increases, then risk decreases C. Is greater than 1.5, then the company is in default D. Is less than 1.5, the company is carrying...

Q:

The following information is taken from the production budget for the first quarter: Beginning inventory in units 900 Sales budgeted for the quarter 342,000 Production capacity in units 354,000 How...