Find a sequence X, Such that X, does not converge (to any XE R) and Y, does converge to 0 where Y, =2X,"
Q: Show that the sequence {f}, where f₁²x) = tan `nx, x70 is uniformly ノ on any interval [a,b], aso but…
A: Given function as fnx=tan-1nx, x≥0
Q: Consider the sequence n²x(1 – nx) x € [0, 1/n] { - fn(x) := elsewhere . Does it converge uniformly…
A:
Q: Consider the sequence {fn(x)}, where sin(nx) fn(x) = 1+ nx Use the uniform norm to show that the…
A: Given: fn(x)=sinnx1+nx To show: fn(x) is uniformly converge on [1, ∞).
Q: (ii) Prove that if a sequence Xn converges to a limit I, then any subsequence of Xnalso converges to…
A:
Q: Determine whether the given sequence converges or diverges. If it converges, calculate its limit. an…
A:
Q: 2. Show that if a > 0, then the sequence (²x²e¬n) converges uniformly on the interval [a, ∞), but…
A:
Q: * Show that the sequence (xn)n>1 in R, where In = 1- Vn' converges to 1.
A:
Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-
A:
Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e
A: Option 3 is correct.
Q: The radius of convergence of about Xo=o (1-メ)
A:
Q: Show that the sequence f.(x)} converges to a limit function (that you should determine) for each XEI…
A:
Q: Find the radius of convergence for n°z"
A:
Q: 3. Prove that the sequence sin(n) (0, 1). converges to n n+1
A: We calculate both limit separately as n tends to infinity.
Q: Find the interval of convergence of ) n°x" and find its sum. n=1
A:
Q: Show that the sequence {fn} where fu(r) = e-n* is uniformly convergent on [a, b), a > 0.
A:
Q: Find the radius of convergence, R, of the ser (-1) R =
A:
Q: The sequence Converges to e Diverges Converges to 0 Converges to 2e Converges to 1
A: First I have written the definition ofconvergent and divergent sequence and then that given sequence…
Q: Show that the sequence of functions {f.} where f,(x)=: 1+ nx „xER is non-uniformly convergent on…
A: Show that the sequence of functions fn(x), where fnx=x1+nx2, x∈ℝ is non-uniformly convergent on…
Q: Determine if the sequence converges or diverges. If it converges, state the limit. arctan n -,n≥2 In…
A:
Q: S sin(n) cos(n)/n converges or 3. Use to sandwich/squeeze theorem to argue whether the sequence 1+n…
A: We need to find if series converges or diverges.
Q: Consider the iteratively defined sequence (x,), where x41 = 3 - 2 and x = 3. Use the Monotone…
A: Monotone convergence theorem: If a sequence monotone and bounded then it is convergent. If the…
Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…
A: Limit of a sequence
Q: Prove that 「+ X,- ズー 2. 71 ,nyo converged number J2 ヒo
A:
Q: Prove, using the formal definition of convergence, that the sequence VnIni converges to 0.
A:
Q: Prove using the ϵ−n0 definition that the sequence Xn=(9−7n)/(8−13n) converges, and find its limit.
A:
Q: The sequence whose nth term is given by x_n=sin(n*pi/6) is unbounded is monotonic converges to a…
A:
Q: What are all of the values of x, such that converges?
A: We have to use GP sum Common Ratio.
Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…
A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…
Q: 1. Prove the sequence {a,} = (1 +-)" Converges to the limit e*, what about the sequence {b,} = (1…
A:
Q: The sequence Converges to e Diverges Converges to 2e Converges to 1 Converges to 0
A:
Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…
A:
Q: A real sequence is defined as {xn} = n/(n+1) ,n : natural numbers. Using the formal definition of…
A:
Q: The sequence {x}=0, where xn (A) True (B) False 20 = is convergent. n!
A:
Q: Show that the sequence of functions {f.} where f,(x)=nxe is non-uniformly convergent on [0,1]. (by…
A: Test for uniform convergence of sequences: Let fn be a sequence of functions such that it converges…
Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to
A:
Q: Let f : A → R and (xn),(Yn) are two sequences converges to c such that Xn, Yn # c, Vn E N. If…
A: We understand this statment by the help of an counterexample .
Q: Use Cauchy Criterion to prove that the sequence {sn} converges where Sn + Sn-1 Sn+1 n > 1, 2 and…
A:
Q: Find limit of a, of the series (–1)"+1 (, Inn-
A:
Q: Let (rn) be a sequence of real numbers. Show that the convergence of (sn) implies theconvergence of…
A: We have to prove that if convergence of (sn) implies the convergence of (|sn|).
Q: If X1, Y1, are two positive unequal numbers and Xn = (xn- 1+ Yn – 1) and y, = Vx, – 1 Ya-1 V n 2 2.…
A:
Q: ** Consider the sequence (xn) in R, where n (-1)". Show that (rn) doesn't %3D converge to any limit.
A:
Q: If Ea, converges absolutely, prove that Ea,² converges.
A:
Q: Given a sequence ( xn ), prove that (xn ) converges to zero if and onlyif the sequence ( |xn| )…
A: From the given information, it is needed to prove that:
Q: Construct a sequence of continuous functions fn : R →→ R such that 0 < fn S 1, limn-o Jo fndx = 0…
A:
Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…
A: Consider the sequence Xn=(-1)n. Then Xn={-1,1,-1,1,-1,1,-1,1,...}. So, Xn does not converges to any…
Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.
A:
Q: 2n+1 4. Use the definition to prove that ) converges.
A:
Q: Find, with justification, a sequence of functions fk : R → R such that (fk) (b) converges uniformly…
A:
Q: Let (x,) be a sequence of real numbers. If for some x e R, (x,) converges to both 7x + 2 and 2x - 13…
A: Which of the following is correct?
Q: Let (X,) be a sequence of real numbers. If for some x e R, (X,) converges to poth 7x + 2 and 2x - 13…
A: which of the following statement is true.
Step by step
Solved in 2 steps with 2 images
- 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!nFollow 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
