Prove that the sequence {sin(nn/3)} does not converge.
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: Find an infinite series that converges to 1/2 ex - 1 dx.
A: Consider the integral: I=∫012ex-1xdx……1
Q: Find an upper bound for the error in using the sum of the first 8 terms to approximate the sum of…
A:
Q: * Show that the sequence (xn)n>1 in R, where In = 1- Vn' converges to 1.
A:
Q: Find the power series (centered at zero) of the function f ( x ) = 3/(4+x2) and state the interval…
A:
Q: Find all numbers x such that the series n=1 converges!
A:
Q: If a geometric series converges to a / (1-r) if |r| < 1, the interval of convergence is
A: If a geometric series converges to a1-r , if |r|<1 { Given }
Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-
A:
Q: +o0 (-1)*n" sin" () Σ 2n n=1
A:
Q: Express the function 1/1−x3 as the sum of a power series and find the radius of convergence and…
A:
Q: Find the largest interval (in x) where the series summation from n = 1 to infinite of xe-nx…
A: Here we use D'Almbert ratio test.
Q: Find x so that x, x + 2, and x + 3 are consecutive terms of ageometric sequence.
A: We have to find the value of x such that x, x+2, and x+3 are consecutive terms of a geometric…
Q: Determine if the sequence converges or diverges. If it converges, state the limit. cos²n an = -,n≥1…
A:
Q: 1 n4 + sin“ n=1
A: To find that the given deries diverges or converges
Q: Find the interval of convergence of the series. (x-1) 5n+ 4 n=0
A:
Q: Prove the absolute value of this series converges.
A: Given series :
Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…
A: We have to prove that xn has a convergent subsequence in each of the given cases.
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: 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: Find an easy expression for the sum of the series on its interval of convergence. (-1)"-'n -x" 2"…
A: Given series is ∑n=1∞-1n-1n2nxn
Q: Show that the series n" n' is convergent. Deduce that lim (2n)! (2n)! n=1
A:
Q: The series 1(-1)" converges to 0. True False
A: We have to find if the given series is converges.
Q: What is the function represented by the power series from k=0 to infinity of ((-1)^k*x^(k+1))/4^k?
A: Power series
Q: Find the limit inferior and limit superior of the sequence {[5 sin n]}.
A: The given problem is to find the limit inferior and the limit superior for the given sequence of {[5…
Q: Show that the series n' (2n)! is convergent. Deduce that lim (2n)! n=1
A:
Q: Find the sum of the convergent series by using a well-known function. Identify the function and…
A: Given series is ∑n=0∞-1n12n+1......(1) We have a well known function ∑n=0∞-1nx2n+12n+1=tan-1x,…
Q: {sin ()} 2
A: Given sinnπ2
Q: Show that the series 71 n' (2n)! is convergent. Deduce that lim 0% (2n)! n=1
A: We have to show that the series ∑n=1∞nn2n! is convergent. Let an=nn2n! Now,…
Q: Find the interval and radius of convergence for each power series. 3* x* (2k)! k=0
A:
Q: Use the equation 1/(1-x) =Σ xn (from n=0 to infinity) for the absolute value of x is less than 1 to…
A:
Q: Find the sum of the convergent series tan - ( m til tan M=1
A: This is a telescoping series. Whose sum is 2/π
Q: The series 2(- 1)"+1 converges n = 1 Select one: True
A: The given series is ∑n=1∞-1n+1
Q: What is the function represented by the power series from k=0 to infinity of (-1)^k(x^k)/(3^k)?
A:
Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…
A:
Q: Find the interval of convergence of the series (–1)"(x+3)*+1 п(п + 1) n=1
A:
Q: b) E, 2n-1
A:
Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…
A:
Q: The sequence {x}=0, where xn 20" is convergent.
A:
Q: Find the exact value that the sequence sin" 1 converges to. (Note n=0 that as usual, sin" x means…
A:
Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to
A: We have to solve
Q: Find the interval of convergence of the series. (x-5) 5n+1 n=0
A:
Q: the root test fails to determine if the series Σ (1 + n= 1 converges or diverges
A:
Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +
A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…
Q: Find the interval of convergence of the series. (3x)" * Σ n2. 10" n=1
A:
Q: The sequence a,=n sin 1 converges Select one: True OFalse
A: We have to check
Q: Determine if the sequence converges or diverges. If it converges, state the limit. = sin (17), n = ₁…
A: We know that 1n→0. We further know that sine is a continuous function. So,…
Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.
A:
Q: 1 Show that the series 2 converges. k=2 k(log k)?
A: Given: ∑k=2∞1klogk2
Q: 5. Show that the sequence Pn = 1 converges linearly to p 0, and the sequence Pn = 10-2" converges…
A:
Q: Show that the series n" (2n)! is convergent. Deduce that lim 0. (2n)! n=1
A:
Step by step
Solved in 3 steps with 3 images
- Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+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