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

Determine whether sum ((5n12 +1)1/3 )/((3n12 -1)1/2) converges or diverges.

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?

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

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

(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^

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