# Calculus 2

posted by .

The following function has a series of the form the sum from n=0 to infinity of c(subn)x^n. Calculate the coefficients c(subn) and express the power series in summation notation.
f(x)=(pi*x)/(pi*x+1)
Thank you so much for your help!!!!

• Calculus 2 -

f(x) = 1 - 1/(pi*x+1)
f' = pi/(pi*x+1)^2
f'' = -2/(pi*x+1)^3
...

f(x) = 0 + pi*x - (pi*x)^2 + (pi*x)^3 - ...
c_n = -(-1)^n pi^n = -(-pi)^n

• Calculus 2 -

Thank you soooooooo much!!!!

## Similar Questions

1. ### Calculus

For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge?
2. ### Calculus III

Which of the following series are geometric series?
3. ### College Calculus (Binomial Series)

Expand f(x) = (x+x^2)/((1-x)^3) as a power series and use it to find the sum of series (SUM from n=1 to infinity) (n^2)/(2^n) PLEASE HELP.
4. ### calculus

state the power series of an appropriate familiar function and use it to calculate the power series of the given function. give answer in sigma notation. All power series have center at 0. f(x)=(e^(-x)^2) -1+(x^2) and g(x)=x cos (x/square …
5. ### Calc II

Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which converges, …
6. ### Calculus 2

Calculate c(sub0), c(sub1), c(sub2), c(sub3), and c(sub4) for the power series the sum from n=0 to infinity of c(subn)x^n that represents f(x)=tanx. Use the first two nonzero terms of the series to approximate the tangent of 1/4 radian. …
7. ### Calculus 2

The function ln(x-1) can be expressed as a Taylor Series of the form sum of c(subn)(x-2)^n. Calculate the formlua for c(subn).
8. ### CALC 2

In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a. Summation …
9. ### CALC 2 pls help!!

In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a. Summation …
10. ### Calculus 2

In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a. Summation …

More Similar Questions