1 1 1 [3 marks] 32.. 1 (a) Find the sum to infinity of the series...
Find the sum of the series, S. Find the sum of the series, S. infinity sigma n = 0 (-1)^n 8^n x^2n/n! S = 8e^-x^2
Determine the interval of convergence for the following series. a/ sum (x-3)k / sqrt k from k=1 to infinity b/ sum (-x)k / k! from k=0 to infinity c/ sum (2x - 21)k / k4 from k=1 to infinity
3) Find the Taylor series centered at 1 for x3 - 2x + 7 4) Find the Maclaurin series for sin X. By using it, show that lim sinx as X + 0 equals 1. X (sing
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0 Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...
Euler found the sum of the p-series with p = 4: (4) = infinity n = 1 1/n^4 = pi^4/90 Use Euler's result to find the sum of the series. Infinity n = 1 (3/n)^4 81/90 pi^4 infinity k = 6 1/(k - 3)^4
Euler found the sum of the p-series with p = 4 zeta(4) = summation_n = 1^infinity 1/n^4 = pi^4/90 Use Euler's result to find the sum of the series. summation_n = 1^infinity (5/n)^4 summation_k = 6^infinity 1/(k - 3)^4
[b] Find a formula for the following sum: S = 3+ 2x + 32 + 4x +...+ (m - 1)an-1 for any n e N, n >1 and any x ER.
(2) Show that sin(x) is the sum of its Taylor series. (3) Find the first three nonzero terms of the Taylor series about 0 for the following functions (a) cos(x2) (b) e (c) tan(x)
It is known that Fourier series of f(x)=x is 2° 2(-1)" + "sin(nx) (n 1 on interval [-T, T). Use this to find the value of the infinite sum 1 - + 1 1 5 7 3
Question 4. (1+(1+2+1) marks] Using the formulas for known series, find the sum of the following series. (b) Σ-1). 3. 25η