6 questions

0/1 pt 20 @ Details Express the sum in terms of geometric series (hint: The pattern repeats on groups of 4 terms, so group zin, zin-1, etc.). Now express the sum as a rational function: Question Help: Video E Written Example Message instructor Submit Question 0/1 pt 9 20 @ Details Question 2 Express the series in terms of elementary functions and find the radius of convergence of the sum. n 3n Radius of Convergence: Power series p1(x) and p2(x) are given below. Pi(x) = 1+3x + 9x2 +27x'+ 81x'+... P2(x) = 1+7x+ 49x2 + 343x3 + 2401x +... Write the first 5 terms of p1(x) + p2(x) below, simplifying any like terms. 1 x *... Write the series compactly using summation notation: 7 = 0 Find the functions to which each series converges to find an expression that represents the final series. (Hint: What transformation was performed upon 1 1 - z = 1+ +x? + x +z'+ ... to generate each series?) P1(I) + p2(I) = 0/1 pt 9 20 @ Details Integrate the given series expansion of f term-by-term from zero to a to obtain the corresponding series expansion for the indefinite integral of f. If f(z) = -524 (1 + 25)2 (-1)"5nx 5n-1 n=0 Suppose the Maclaurin series f(a) is f(z) = (2)". 1. f(t) at = [ Find the Maclaurin series for the following. Question Help: Video @ Written Example M Submit Question f'(z) = > 7 - 1 f(3z) => Question Help: Video @ Written Example Message instructor Submit Question . Question 4 GO/1P If f(z) = >2x" and g(z) - Inx", find the power series of f (z) g(I). 7 0