(b) Find the sum of the series and its radius of convergence (-1)n + 1(x-1)n = n=1 R= 1 (c) Use a graphing utility and 50 terms of the series to approximate the sum when x - 0.5. (Round your answer to six decimal places.) 50 -1n 1 n=1 (d) Determine what the approximation represents The sum from part (c) is an approximation of Determine how good the approximation is. (Round your answer to six decimal places.) error0
(b) Find...
(1 point) Find a function of x that is equal to the power series En= n(n + 1)x" = for <x< Hint: Compare to the power series for the second derivative of 1-X (1 point) Find a formula for the sum of the series (n + 1)x" n=0 101+2 for –10 < x < 10. Hint: D,( *) = " " 10n+1
2 Q.1) Find the sum of the series An=1 (n+1)(n+3) (10 Pts.)
Find the Fourier series of the following function, and calculate the sum of rn. n=1 f(x) = 12,2 if 0<r<\ if-1< 0 f(x + 2)-f(x)
(a) Find the partial sum S, and the sum S. of the series, (b) Graph the first 10 terms of the sequence of partial sums and a horizontal line representing the estimated S.. 6 (2) In=1(sin 1)" (1) 2 = (n+1)(n+2)
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
11) Find the sum of the arithmetic series if a, = 5, 4, = -160, and n = 21. -4706 12) Find all the values of x and y for which 3, x, y is an arithmetic sequence and x, y, 8 is a geometric sequence. 222 222 13) Find the value of y that makes this a geometric sequence: y+1, y, y-4.
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...
n2-1 Find the sum of the series (n=1 n=1 (n2 +1)2
write a recursive algorithm to find the sum of the first N terms of the series 1, 1/2, 1/3, ... 1/N