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.

Express the function F(x) = 7x/((2x-1)(x+3)) as a power function centered around 0 and find the Interval of Convergence

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)

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

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^

Express 1/(1+ x*) as the sum of a power series and find the interval of convergence. Solution:

(-1)* Estimate the value of the convergent series with an absolute error less than 10-5. k! + 2 k=1

Determine whether the alternating series E (-1)^+1° converges or diverges. n = 1 n3