# What is the interval of convergence of the series #sum_(n=0)^oo((-3)^n*x^n)/sqrt(n+1)#?

Using the Ratio Test

#lim_{n to infty}|{a_{n+1}}/{a_n}| =lim_{n to infty}|{(-3)^{n+1}x^{n+1}}/{sqrt{n+2}}cdot{sqrt{n+1}}/{(-3)^nx^n}|#

By eliminating common elements,

By dividing three,

We must now examine the endpoints.

which, according to the Alternating Series Test, is a convergent alternating series.

By signing up, you agree to our Terms of Service and Privacy Policy

The interval of convergence of the series is (-1/3, 1/3).

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the interval of convergence of #sum_1^oo [(2n)!x^n] / ((n^2)! )#?
- What is the radius of convergence of the MacLaurin series expansion for #f(x)= sinh x#?
- How do you find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a f(x) = cos(x), a= pi/4?
- How do you find the taylor series for #f(x) = cos x # centered at a=pi?
- What is the Maclaurin series for #(1-x)ln(1-x)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7