Need help writing one power series
Please let a = 23;
Show work as well, thank you!!
1. Invent a distinctive positive number o. (a) Determine the interval in which the series Σ nan converges ab- solutely. ,n (b) What is the fourth partial sum of m- 7l Σ nam. (c) Let f(r) Compute the first four terms of a power series for f'(x) (d) Let f(z) = Compute the first four terms of a power nan series for /f(x) da
1. Invent a distinctive positive...
1 6. Using the power series = Σ c" |x | < 1, find a power series about O for 1 х n=0 1 and state the radius of convergence. (2 - x)2
I need help on questions 17, 21, and 25.
Thanks!
In Exercises 9-24, a power series is given. (a) Find the radius of convergence. (b) Find the interval of convergence. 17. Σvnx n=0 18. Σ n=0 19. 31 (x – 5)" n! n=0 20. Σ(-1)"n!(x – 10) n=0 21. η2 n=1 In Exercises 25 – 30, a function f(x) = ax" is given. (a) Give a power series for f'(x) and its interval of conver- gence. (b) Give a power...
Find the power series for with center 7. Σ Preview D=0 The series is convergent on the interval Preview
A power series solution is about x=0 of the
differential equation y"-y=0 is
A power series solution about x = 0 of the differential equation y'-y=0 is Select the correct answer. YOU MUST SHOW WORK ON SCRATCH PAPER AND y=Σ * (2x)! +,Σ_o 28 +1 X (2λ + 1)! νεεΣ. *(2x) +σ,Σ. x (2k +1) γεςΣ. * (26) +0, Σ., και 28-1 (2-1): v=c,Σ. ΚΙ(2x) +σ,Σ. ** (2x-1) Ο γιο,Σ: * (2x) +c, Σ. x 28 (2+1)
Please help solve all of them!
DETAILS 1. [-/5 Points) MY NC Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) 1 + x Σ provided 1x1 no 2. [-/5 Points) DETAILS MYN Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) 5 f(x) 1 + Σ provided fx < no 3....
Write as a single Power series. Σ=1 non-1 ΧΟ n=0 h O None of them ΧΟ k=1 ΟΣ-0 kak k=0 ΟΣΟ (k - 1) *
Use the power series itxË (-1)"X", Ixl < 1 -n=0 to determine a power series for the function, centered at 0, 14 02 7 f(x) (x + 1) dx2 ( x + 1 00 f(x) no Determine the interval of convergence. (Enter your answer using interval notation.) 3. [-17.69 Points] DETAILS LARCALC11 9.2.061. Find all values of x for which the series converges. (Enter your answer using interval notation.) 00 (8x)" n=1 For these values of x, write the sum...
3 is represented as a power series: (1 point) The function f(x) 1+36x2 Σ f(x) - n-0 Find the first few coefficients in the power series. CO CI C2 C3 CA Find the radius of convergence R of the series R =
Need some help with SERIES SOLUTION - 2nd ORDER EQUATION For the differential equation, (1) a. Calculate the indicial equation for the power series solution (Answer in a quadratic polynomial in terms of c.) b. Calculate the solutions of the indicial equation found above. c. Calculate the point from the above equation (1) as i. ORDINARY POINT ii. REGULAR SINGULAR POINT iii. IRREGULAR SINGULAR POINT We were unable to transcribe this imagey-Σ@m(z _ 4)nte We were unable to transcribe this...