+∞ n(3x + 2)" Consider the power series > n³ +4 n=1 1. Show that the series is absolutely convergent when x = −1. 2. Find the interval of convergence of the power series.
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- 1. use integration along with knowledge of geometric series to find the power series of arctan(2x/3)2. what values of x is the power series converging (interval of convergence)Find the series radius and interval of convergence. What values of x does the series converge absolutely, conditionally?find a power series that represents the function by modifying the base series for 1/1-x Then, find the interval of convergence of the power series:
- A series converges to a sum of 13. The first term has a value of 3. Algebraically determine the exact value of the common ratio.Find a power series for the function, centered at c=3, for the function f(x)= 4/3x+2. State the interval of convergence. Please show all work thank you.Now instead integrate the power series for 1/1-x to find a power series representation for ln(1-x0. What is the interval of convergence for this power series? Then use it to determine the exact value of ∞Σ n=0 1/(n+1)2^(n+1).
- 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.If a power series cn(x + 3)^n converges conditionally when x = 3, find the radius of convergence. Explain your answer.Find a power series representation for the function. Determine the interval of convergence. f(x) = 1/(6+x)
- Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x 14x2 + 1 Then determine the interval of convergence enter using interval notationUsing 1/(1-x), find a power series for f(x)= 3/(2x+5) and its interval of convergence. Write step by step.Find the interval of convergence of the power series. ( Be sure to include a check for convergence at the endpoint of the interval.) Step by step solution.