# calculus

posted by .

write a power series for e to the 2x and find the interval of convergence

• calculus -

Since e^x = 1 + x + x^2/2! + x^3/3! + ...

e^2x = 1 + 2x + 4x^2/2! + 8x^3/3! + ...

It converges for all x.

## Similar Questions

1. ### calculus-- need help desperately!

The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=5 is given by f^(n) (5)= (-1)^n(n!)/((2^n)(n+2)), and f(5)=1/2. Write third degree Taylor …
2. ### CALCULUS

find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)
3. ### CALCULUS-URGENT

find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)
4. ### CALCULUS-URGENT- no one will respond!!!

find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)
5. ### Calculus

Can someone prove (informally) the following theory: If there is a differentiable function, f, that is represented by a Taylor series, T, then the convergence interval for series T is identical to the convergence interval for the term-by-term …
6. ### Calculus

a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of …
7. ### Calculus 2

Find the radius of convergence and interval of convergence of the series. n=2 series to infinity (-1)^n * x^n+6/n+7 R= ?
8. ### Calculus

What is the radius of convergence of the power series (((2n)!x^(n))/((2n-1)!)), and what is its interval of convergence?
9. ### calculus

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 of the series at the endpoints in order to determine the interval of convergence. …
10. ### Calculus 2

Find the radius of convergence and interval of convergence of the series. There is an infinity sign on top of the summation symbol and "n=1" underneath it. To the right of the summation symbol is x^n/5n! How would you find the radius …

More Similar Questions