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4 years ago

Does the following infinite series converge or diverge?

1 answer:

7 0

The nth term is (presuming the denominator on the first is a typo)

$-\dfrac{n}{(-3)^n}$

The ratio of successive terms is

$\dfrac{ \frac{n+1}{(-3)^(n+1)}}{\frac{n}{(-3)^n}} = \frac{n+1}{-3n}$

The limit is -1/3, absolute value less than 1, so the series converges. It has a sum -- that's what converges means.

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There is only one correct answer, regarding both questions.

Georgia [21]

The answer to number one is C
and the answer to number two is A

6 0

3 years ago

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

dlinn [17]

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-5\\ n=10\\ a_{10}=13 \end{cases} \\\\\\ a_{10}=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies \boxed{2=d}$

7 0

3 years ago

At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequa

Leya [2.2K]

Answer:

t≥-25

Step-by-step explanation:

this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.

8 0

3 years ago

Find the value of x in a triangle . If the hypotenuse of the triangle is 10 , the opposite is x+2 and the adjacent is x.

Sauron [17]

Answer:

x = 6

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² + (x + 2)² = 10² ← expand parenthesis on left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

however, x > 0 , then x = 6

8 0

2 years ago

A professional basketball player may be more than two feet taller than an olympic gymnast. how would their vertebra compare?

vovangra [49]

The <u>correct answer</u> is:

The basketball player's vertebrae may be bigger than the gymnast's.

Explanation:

There are several factors that influence height; for one, the length of the legs affects one's height.

Additionally, however, if someone has bigger vertebrae, then they would be taller than another person.

4 0

3 years ago

Read 2 more answers