Question: Could someone please check my work 1. Suppose that lim S = 0 . If (tn) is a bounded sequence, prove that lim (Sn .

Could someone please check my work

1. Suppose that lim S = 0 . If (tn) is a bounded sequence, prove that lim (Sn . tn) = 0. Suppose lim Sn = 0 and (tn) is a bounded sequence. Since (tn) is bounded, 3m > 0 such that |tn) 0, 3N E N such that Vn > N, Isn - 0| lal . 125/ 5 12071 . 1251 = 127. 281 = 10- 27. us/'N 0, N E N such that Vn > N , Isn - 0| = |snl N, Isn . tn - 0| = Isn . tal = Isnl . Itn)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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 Mathematics Questions!

In this Challenge, you are tasked with helping a small, rural town modernize its vote-counting process. You will be given a set of poll data called election_data.csv. The dataset is composed of three...

Could someone please check my work Prove That The sequence is Monotone and bounded . Then find The limit. Sn= 2 and s.. = 4 (5, +5) for all neIN 5 , = 2 5 2 : 7 ( 2 + 5 ) . 7 = 1.75 53 = 4 ( 7+ 5 ) =...

Could someone please check my work 1. If (Sn) is an unbounded increasing sequence, then lim Sn = + co. Let (Sn) be an increasing sequence and suppose that the set S = {Sn : n E N) is unbounded. Since...

Could someone please check my work Suppose ( S,) is a convergent sequence with lim SA = S. Prove lim ( K. Sn)- Ks and lim ( K+ 5. )= K+ s, for any KERR and KEIR - by definition of convergence Given...

Could someone please check my work 1. Prove that x is an accumulation point of a set S iff there exists a sequence (Sn ) of points in S\\{x} such that (Sn) converges to x . . ( # ) x is an...

Could someone please check my work comp Theorem 4.2.1 lim ty = t. Then Suppose that (s,) and (1.) are convergent sequences with lims, = s and (a) lim (S, + 1) = 8+ 1. (b) lim (ks.) = ks and lim (*...

Could someone please check my work Prove That The Sequence is monotone and bounded. Then find The limit. Sa = and Snap = 4 25. + 1 for ell nerN S, = 2 5 , = 472( 2 ) + 1 = 15 = 0.5 5 1016 9944 Sa # 4...

Could someone please check my work HWLO QL2 Prove That The Sequence is moncrone and bounded. Then find the limit. Sa=aand Snap = 4 25, +1 for all ne IN S, = 2 S, * 4 2( 2)+ 1 = 15 = 0.5 5 1016 9944...

Could someone please check my work Let /: D - R and f: D - R , and let c be an accumulation point of D . Please state all definitions and theorems that you will need: If lim fux) = L, lim g(x) = M ....

Could someone please check my work and let me know if I am correctly using all of the included theorems that are referenced in the proof Please state all definitions and theorems that you will need:...

Could someone please check my work and make sure I'm using the correct theorems Please state all definitions and theorems that you will need: Theorem 5.1.13 Let f : D -+ R and g: D - R and let c be...

An experiment was conducted to determine whether there is a difference between the success rates from treating carpal tunnel syndrome with surgery and with splinting. The success rate for 73 patients...

Towing Company has budgeted sales for the next six months as follows: On average, 32% of the sales on account are collected in the month of sale, 40% are collected in the month following sale, 16%...

11. A metallurgist added eight substances in various combinations to seven samples of molten aluminum for the purpose of producing aluminum alloys. Th e metallurgist was interested in producing an...

9. Which among the following phenomena exhibit/s a Fibonacci number sequence? i. The sum of the numbers in the diagonals of the Pascal's Triangle. ii. The number of petals of most flowers like Lily,...

A circus team, "The Feather-Fall Four" wish to perform a trick where a team member, Nanbali, is launched straight up into the air to a height of 6.00 m from the ground when. two of the other team...

Suppose the monetary base is 2000 dollars, currency held by the public is 600 dollars, bank excess reserves are 200 dollars, and the required reserve ratio is 10 percent. 1- Compute the amount of...

In Ramadan month and in Christmas, consumers increase their preferences for cash versus demand deposits. Explain the effect this has on 1- Primary deposits 2- Derivative deposits 3- Credit multiplier...

6. Which type of symmetry is best illustrated in the figure below: A. Bilateral Symmetry B. Radial Symmetry C. Equilateral Symmetry D. Asymmetric or No Symmetry 7. The ratio between consecutive terms...

Write a program to wish happy birthday to a student. Firstly, take today month and day as an input and secondly take birthday as an input in the form of month and day. If the input day and month...

4. I try to make them feel what I really mean (1 is related to the visionary, 2 to the logical, 3 to action and 4 to the emotional).

4. What is the goal of the others in the network?

2. What we can learn from the past