we are given series as
we can use series formula
we can write as
we can plug x=-2 in series formula
and we get
...........Answer
Evaluate the following infinite series. so (-1)"+12n-1 2n=0 n! 2e-2 e-2 0 -2e-2 0-5e-2 O none...
Evaluate the following infinite series. no (-1)74121-1 e-2 2e 2 none of the above or below 0-te 2 2e 2
Evaluate the following infinite series or state that the series diverges. § [(9)*--(0)*] k=0 Evaluate the series or state that the series diverges. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. § (209)*--(8)*1- (Simplify your answer.) k= 0 O B. The series diverges.
Which of the following series diverges? n +2 2n -1 n1 n+3 O A. 2 B. O C. 1,3 O D. 1, 2 OE. 2, 3 F. None O G. O H. 1,2,3 Find the sum of the series A. B. OC. 1/10 D. 1/2 3/2 3/4 OE. 1 F. 5/12 OG. 1/4 H. Divergent Which of the following series converges? oo 2n 1.Σ n 1 23n nE1 (n+ 1)3 n+ 1 3. O A. None O B. 2 O...
Pt 1
pt 2
pt 3
pt 4
Please Answer every question and SHOW WORK!
Determine whether the series n-1 Σ (2n)! 2". (2n! converge or diverge 1. both series converge 2. only series II converges 3. only series I converg es 4. both series diverge Determine whether the series 2! 1515.9 1-5.9-13 3! 4! 7m 1.5.9..(4n -3) is absolutely convergent, conditionally con- vergent, or divergent 1. conditionally convergent 2. absolutely convergent 3. divergent Determine which, if any, of the...
3. The following series is attributed to Newton. It can be used to calculate r. n-0 (n!) (2n 1) 24n+1 (a) (2 points) Prove that the series converges. (b) (2 points) Compare S5 to the actual value of π.
3. The following series is attributed to Newton. It can be used to calculate r. n-0 (n!) (2n 1) 24n+1 (a) (2 points) Prove that the series converges. (b) (2 points) Compare S5 to the actual value of π.
1 1. Find the exact sum of the following infinite series as indicated below: -1 1 1 1 1 + n(-4) 2(16) 3(64) 4(256) a. Let f(x) = 2n=1 (-1) x". I n a b. Find the power series for the derivative f'(x), and observe that it is a geometric series. Find its first term and common ratio. c. Use the formula 1-r to find an algebraic expression for f'(x). d. Integrate to find an algebraic expression for f(x). Make...
4.1 The following infinite series can be used to approximate e: 2 +3 + 2 e = 1 x + 3! n! (a) Prove that this Maclaurin series expansion is a special case of the Taylor series expansion [(Eq. (4.7)] with x (b) Use the Taylor series to estimate f(x) 0 and h x. e at x+1 1 for 0.2. Employ the zero-, first-, second-, and third-order versions and compute the e, for each case.
4.1 The following infinite series...
(1 point) Use power series to solve the initia-value problem 2n+1 2n Answer: y- n-0
(1 point) Use power series to solve the initia-value problem 2n+1 2n Answer: y- n-0
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
1. Determine if the following series converge or diverge. If they converge give the value of the series. q-n+24n+1 n=1 37n 2N=14+4n 2 72 C. 271
1. Determine if the following series converge or diverge. If they converge give the value of the series. q-n+24n+1 n=1 37n 2N=14+4n 2 72 C. 271