Using 1/(1-x), find a power series for f(x)= 3/(2x+5) and its interval of convergence. Write step by step.

Use the geometric series to derive a power series for the function f(x) = 1 / (1-x). What is the radius of convergence for this power series?

Give an example of a series that converges by the integral test.

Verify that Jp+1(x) + 2J½ (x) – Jp-1(x) = 0 Tip: Compare the series of Jp+1(x) – Jp-1(x) and – 2J½(x) = 0

Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were , you would write . Also indicate the radius of convergence.   1/(1-x5)

Find the interval and radius of convergence for the given power series. n=1 (x-4)" n( - 8)" The series is convergent on the interval: The radius of convergence is R =

(1+x)-3=1-3x+6x2-10x3........ Is this series convergent or divergent? Simply explain why

The difference of two convergent series is not necessarily a convergent series.

Find the power series (centered at zero) of the function f ( x ) = 3 /4 + x2 and state the interval of convergence. Write the first terms of the power series. You do not have to express the series in sigma notation. Don't forget to state the interval of convergence.

Proceed as in this example to rewrite the given expression using a single power series whose general term involves xk. 8 k=0 n=1 no-1- n=0 9cx^