True of False
(g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3.
(h) If the terms an approach zero as n increases, then the series an converges?
(i) If an diverges and bn diverges, then (an + bn) diverges.
(j) A power series always converges at at least one point.
(l) The series from ∞ to n=1 2^ (−1)^n converges?
True of False (g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3. (h) If the terms an approach zero as n increases, then the series an converges? (i) If an diver...
1. Decide if the following statements are true or false. Give an explanation for your answer. (a) If 0 < an < bn and Σ an converges, then Σ bn converges (b) If 0 < an < bn and Σ an diverges, then Σ bn diverges. (c) If bn an 0 andbcoverges, then an converges (d) If Σ an converges, then Σ|an| converges (e) If Σ an converges, then linn lan +1/a (f) Σχ00(-1)"cos(nn) is an alternating series (g) The...
(1 point) Find the interval of convergence for the following power series: n (z +2)n n2 The interval of convergence is 1 point) Find the interval of convergence for the following power series n-1 The interval of convergence is: If power series converges at a single value z c but diverges at all other values of z, write your answer as [c, c 1 point) Find all the values of x such that the given series would converge. Answer. Note:...
Please show work, thank you. 1) Find a power series and radius of convergence for X x + 10 lim 2) Suppose that [bn+1xn+1 bnxn converges for all || < 2. Use the ratio test to conclude that <1 n-00 bn. -xh n=0 n + 1 converges for |«/ < 2.
Determine for what values of x the power series (-1)"2"(x+1)" converges. 3"n What is the interval of convergence? What is the center? What is R the radius of convergence?
k=1 Question 4. Suppose that the power series ax (x – 2)* converges at x = 5 and diverges at x = -7. Write four real numbers at which the series converges and two real numbers at which the series diverges. What can you say about the radius of convergence? Explain your answers clearly.
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4 (1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
#3 n-1 Determine whether the series 2 35 n=1 converges or diverges. If it converges, find its sum. #41 00 n-1 Analyze for convergence (6) NO -0") . Find the sum in case the series converges. n=1
[3] 2. Find the radius of convergence of the power series z" 5(n/2) n=1
(2+3+1+1+1=8 points) Roughly, the Limit Comparison Test allows one to determine whether a given DO series an converges or diverges based on the computation of the limit an L = lim no ba 00 where on is another series. In this exercise, the Limit Comparison Test is used to determine whether the series shown below converges or diverges: yาง m4 +5n - 4 1. Write your choice of bn (Your answer should be in terms of n and simplified fully.)...
Q [3] 2. Find the radius of convergence of the power series zn 5(n/2) n=1