The Maclaurin series for a function is given by (-3)^-¹ (-3) -1 71 converges to f(x) for x < R, where R is the radius of convergence of the Maclaurin series. AX 11111 and (b) Write the first four nonzero terms of the Maclaurin series for f, the derivative of f. Express as a rational function for x < R.

Find the power series for the functions below. Write your answers with the sum starting at n=0  a) f(x) = ln (x+1) b) r(x) = x^4/(1+2x)^3 ( 1+2x in the parenthesis raised to the power of 3).

Find the sum of the series for the values of x, for when the series converges.

Evaluate the infinite series by identifying it as the value of a derivative of a geometric series. n(n 1) 5n ∞ n=2 = Hint: Write it as f" 5 where f(x) = ∞ n=0 n x" 25