Problem 5 Discuss the convergence of the following sequences: (a) an - 7 TL = n...
Problem 3 Discuss the convergence or divergence for each of the following sequences: 3 1. an n+1 1 3. Show that lim
7. (25) Solve the following problems. (a) Find the limit (b) Find the interval of convergence of the following power series 0O TL Tl n-1 (c) Find the sum of the following power series and determine the largest set on which your formula is valid n= 1 (d) Let f(x) = cosa. Find T6(2), the Taylor polynomial of f at zo = 0 with degree 6 (e) Calculate the Maclaurin series for the following functio f(x) = In 7. (25)...
number 4 1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
Problem #10: Which of the following sequences converge? (i) an (-1)n+1 n n2 - 7 (-1)" n2 n? - (iii) an = cos(NT) (iv) an= sin(nn) (ii) an= -9 (A) (i) only (B) (ii) only (C) (i) and (iv) only (D) (i) and (iii) only (E) (ii) and (iii) only (F) (ii) and (iv) only (G) all of them (H) none of them
Problem 5. Discuss the convergence of the following series by calculating the radius of convergence R and checking what happens at the "boundary points" < = +R. Do these series converge uniformly on any of the intervals (-r, R], [-R,r), or [-R,R] where 0 <r<R?
Please answer a, c, e 7.1. For each of the sequences, prove convergence or divergence. If the sequence converges, find the limit. (c) an = cos(n) (e) an = sin(1) (b) an = (-1)" (d) an = 2 – 2.izza (a) an = e in
(1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA...
I need help with problem #9 For Questions 5 through 7, determine convergence or divergence of the series using any test of your choice. If the series is geometric, give its sum. You must verify that all assumptions of the test you choose are satisfied. 5. (8 points) § (193) 6. (10 points) { $s 8. Find the radius of convergence and interval of convergence for the series below: (a) (6 points) mal (b) (6 points) { }(22+1)* sin 9....
Problem 1 convergence test used. Discuss convergence or divergence of the series. If convergent state the (a) ¿ In(n) In(n) In(n) + 2 n=1 (b) 2 (c) n!
11. Determine whether the following sequences are convergent or divergent. Find the limit in case of convergence. (-1)" (n2 + 1) - Vn+1 - Vm, 1+(-1)”, 2n2 +3 cos 7.