PLEASE HELP!!!! WILL GIVE BRAINLIEST!! 30 POINTS!!

\sum_{n=1}^{\infty } ((-1^n)/n)x^n Find the interval of convergence.

Lorico [155]

Answer:

(-1,1).

Step-by-step explanation:

We need to calculate $\lim_{n \to \infty}\frac{| a_{n+1}|}{| a_{n}|} = \frac{1}{R}$ where R is the radius of convergence.

$\lim_{n \to \infty}\frac{\frac{|(-1)^{n+1}|}{|n+1|}}{\frac{|(-1)^{n}|}{|n|}}$

$\lim_{n \to \infty}\frac{\frac{1}{|n+1|}}{\frac{1}{|n|}}$

$\lim_{n \to \infty}\frac{|n|}{|n+1|}$

Applying LHopital rule we obtaing that the limit is 1. So $1=\frac{1}{R}$ then R = 1.

As the serie is the form $(x+0)^{n}$ we center the interval in 0. So the interval is (0-1,0+1) = (-1,1). We don't include the extrem values -1 and 1 because in those values the serie diverges.

4 0

4 years ago

Explain why the expression 7•3x is not equal to the expression 21x

Firdavs [7]

Working out the expression 7(3ˣ) is first to calculate the value of 3ˣ then multiply the answer to 7.

For example, let x = 2
Then 7(3ˣ) = 7(3²) = 7 × 9 = 63

With the same value of x = 2, calculating 21ˣ = 21² = 441, which isn't the same answer with the expression 7(3ˣ)

5 0

4 years ago

What is negative one eighth of a number is -3/4 as an equation? will name the brainliest!

topjm [15]

Answer:

The equation is $-\frac{1}{8}$ x = $-\frac{3}{4}$

Step-by-step explanation:

The Equation is formed from two sides equal to each other

In the algebraic statement "is" means equal

In the algebraic statement "of" means times (×)

∵ One eighth means $\frac{1}{8}$

∴ Negative one eighth means $-\frac{1}{8}$

→ Assume that the number is x

∵ "of" means times

∴ Negative one eighth of a number = $-\frac{1}{8}$ × (x)

∴ Negative one eighth of a number = $-\frac{1}{8}$ x

∵ Negative one eighth of a number is $-\frac{3}{4}$

→ "is" means equal, so the left side is $-\frac{1}{8}$ x and the right side is $-\frac{3}{4}$

∴ $-\frac{1}{8}$ x = $-\frac{3}{4}$ ⇒ Equation

∴ The equation is $-\frac{1}{8}$ x = $-\frac{3}{4}$

7 0

3 years ago

Samantha is preheating her oven before using it to bake. The initial temperature of the oven is 70° and the temperature will inc

spin [16.1K]

The answer is 410°

You have to multiply 17x20 and then add 70 because that’s the initial temp.

5 0

3 years ago

DUE TODAY SOMEONE HELP ME!!!!!!!!! When solving an equation with an exponent that is a variable can I ONLY distribute the number

DIA [1.3K]

Answer:

Option C

Step-by-step explanation:

If we were to consider this question as a whole, all we are being asked is to find an expression equivalent to 2 * ( 5 )^x, as all other function are expressed in the same f ( x ) format. Now all we have to thing about are the expression that = 2 * ( 5 )^2x;

$2( 5 )^2x =\\2( 5^2 )^x =\\2( 25 )^x\\\\Solution - Option C$

Hope that helps!

8 0

3 years ago