QUESTIONS 5 AND 6 PLEASE QUESTION 6 RELIES ON QUESTION 5 TO GET THE ANSWER 5. Let (xn)neN be a sequence in R. For each n in N, letx1 +x2 + .+ Xn...Yn =nShow that if (xn)neN converges to x, then (yn)neN converges to x. [Hint:Writex1 +x2+··+ XnnxYn - x =(xno+1 - x) + + (xn - x)(x- Oux) + + (x-Ix)...|nand, given ɛ > 0 and suitably choosing no,|x1 - x++ |Xno-xп - поE...lyn – x| <Now take the limit superior of both sides of this inequality.]6. Refer to Exercise 5. Show that there are nonconvergent sequences (Xn)neNfor which (y,)neN converges. [Hint: Consider (0, 1, 0, 1, 0, 1, ...).]

Name: QUESTIONS 5 AND 6 PLEASE QUESTION 6 RELIES ON QUESTION 5 TO GET THE AN
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: QUESTIONS 5 AND 6 PLEASE QUESTION 6 RELIES ON QUESTION 5 TO GET THE ANSWER 5. Let (xn)neN be a sequence in R. For each n in N, letx1 +x2 + .+ Xn...Yn =nShow that if (xn)neN converges to x, then (yn)neN converges to x. [Hint:Writex1 +x2+··+ XnnxYn - x

Answered: Image /qna-images/answer/5ac2cb0d-08c8-4c49-9eb7-50549a5b9514.jpg

Math

Advanced Math

. Let (xn)neN be a sequence in R. For each n in N, let X1 +x2 + +Xn Yn Show that if (xm)nɛN converges to x, then (yn)neN converges to x. [Hint: Write x1 +x2 + · ··+Xn nx Yn -x = (x- Oux) +.+ (x-Ix) (xno+1 - x) + + (xn – x) n and, given ɛ > 0 and suitably choosing no, |x1 - x++xno - x| п - по E. ... lyn – x| < Now take the limit superior of both sides of this inequality.] 5. Refer to Exercise 5. Show that there are nonconvergent sequences Xn)neN for which (yn)neN Converges. [Hint: Consider (0, 1,0, 1, 0, 1, ...).]

. Let (xn)neN be a sequence in R. For each n in N, let X1 +x2 + +Xn Yn Show that if (xm)nɛN converges to x, then (yn)neN converges to x. [Hint: Write x1 +x2 + · ··+Xn nx Yn -x = (x- Oux) +.+ (x-Ix) (xno+1 - x) + + (xn – x) n and, given ɛ > 0 and suitably choosing no, |x1 - x++xno - x| п - по E. ... lyn – x| < Now take the limit superior of both sides of this inequality.] 5. Refer to Exercise 5. Show that there are nonconvergent sequences Xn)neN for which (yn)neN Converges. [Hint: Consider (0, 1,0, 1, 0, 1, ...).]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

See similar textbooks

Similar questions

Calculate the first eight terms of the sequences an=(n+2)!(n1)! and bn=n3+3n32n , and then make a conjecture about the relationship between these two sequences.
Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n • In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value of n that ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“ from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 65. List the first four terms of the sequence. an=5.7n+0.275(n1)
Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n • In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value of n that ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“ from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 66. List the first six terms of the sequence an=n!n
Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose ‘seq(” from the dropdown list. Press [ENTER] • In the line headed “Expr:” type in the explicit formula, using the [X,T,,n] button for n• In the line headed ‘Variable” type In the variable used on the previous step. • In the line headed ‘start:” key in the value of n that begins the sequence. • In the line headed “end:’ key in the value of nthat ends the sequence. • Press [ENTER] 3 times to return to the home screen. You will see the sequence syntax on the screen. Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. Using a TI-83, do the following. • In the home screen, press [2ND] LIST. • Scroll over to OPS and choose “seq(“ from the dropdown list. Press [ENTER]. • Enter the items in the order “Expr’, Variable’, ‘start”. end separated by commas. See the instructions above for the description of each item. • Press [ENTER] to see the list of terms for the finite sequence defined. Use the right arrow key to scroll through the list of terms. For the following exercises, use the steps above to find the indicated terms for the sequence. Round to the nearest thousandth when necessary. 63. List the first six terms of the sequence. an=n33.5n2+4.1n1.52.4n
Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+