## What is the interval of convergence of the series?

Worked example: interval of convergence.

The interval of converges of a power series is the interval of input values for which the series converges.

## How do you find the interval of convergence of a Maclaurin series?

Finding radius of convergence of a Taylor series (KristaKingMath

## How do you find the domain of convergence?

Examples of Determining Domain of Convergence of Power Series

## How do you find the rate of convergence?

One approach is to calculate μ=limn|xn+1−L||xn−L|. Here we have μ=limn|sin3n+1sin3n|=limn|3n+13n|=1, hence we have what is known as sublinear convergence. As you say, for small x we have sinx≈x, so for large n we have sin3n≈3n. Then whatever terminology you have for 3n approaching zero as n goes to infinity.

## Is 1 N convergent or divergent?

n=1 an converge or diverge together. n=1 an converges. n=1 an diverges.

## What is the interval of convergence when R 0?

If the power series only converges for x=a then the radius of convergence is R=0 and the interval of convergence is x=a . Likewise, if the power series converges for every x the radius of convergence is R=∞ and interval of convergence is −∞<x<∞ − ∞ < x < ∞ .

## Can radius of convergence be negative?

The Radius of Convergence of a Power Series. Definition: The Radius of Convergence, is a non-negative number or such that the interval of convergence for the power series $\sum_{n=0}^{\infty} a_n(x – c)^n$ is $[c – R, c + R]$, $(c – R, c + R)$, $[c – R, c + R)$, $(c – R, c + R]$.

## How do you find the sum of an infinite series?

Sum of an Infinite Geometric Series, Ex 1 –