All categories

3 years ago

State why the series is convergent or divergent, and if it is convergent, find the sum.

Mathematics

1 answer:

MatroZZZ [7]3 years ago

8 0

Answer:

Converges, 10

Step-by-step explanation:

∑ 5 / 2ⁿ⁻¹

= ∑ 5 (½)ⁿ⁻¹

This is a geometric series with a₁ = 5 and r = ½. Since |r| < 1, the series converges to:

S = a₁ / (1 − r)

S = 5 / (1 − ½)

S = 10

You might be interested in

A submarine lies 3 kilometers from the path of a target ship. The sub’s torpedoes have a range of 5 kilometers. For what distanc

aev [14]

The distance along the path of the ship be within the range of the torpedoes is 4 kilometers.

Explanation:

The submarine lies 3 km from the target ship.

Let B denotes the target ship and C denotes the submarine.

Let AC denotes the the target ship would be within the range of the torpedoes.

The image attached below illustrates that the distance between submarine and the target ship and the range of the torpedoes.

Let BC denotes the distance between the target ship and the submarine. Let AC denotes the range of the torpedoes.

To determine the length of AB, let us use Pythagorean theorem,

$AC^{2} =AB^{2} +BC^{2}$

Substituting the values of BC = 3 and AC = 5, we have,

$5^{2} =AB^{2} +3^{2}$

Squaring the terms, we get,

$25 =AB^{2} +9$

Subtracting both sides by 9, we have,

$16 =AB^{2}$

Taking square root on both sides,

$AB = 4$

Thus, the distance along the path of the ship be within the range of the torpedoes is 4 kilometers.

5 0

4 years ago

Any help is appreciated!

DedPeter [7]

Answer:

1. 10 x 12 = 120 2. 4 (48/12)

6 0

3 years ago

Which of the following are not linear functions? Place a check mark in the box next to each equation that is not a linear functi

insens350 [35]

Answer:

D. y = 2x² + 1

E. y = x²

Step-by-step explanation:

Linear function:

A linear function has the following format:

$y = ax + b$

In which a is the slope and b is the y-intercept. A constant function is linear, as it is the special case in which a = 0.

In this question:

In options D and E, the highest exponent of x is 2, which means that they are not linear functions, and so these options are the answer.

5 0

3 years ago

What is the value of X

andrezito [222]

The value of x is X=7

3 0

3 years ago

How are a common denominator and a common multiple alike and diferent

marin [14]

Answer:

To find a common denominator of two fractions, you have to find a number that both denominators of the given fractions will divide into. And to find a common multiple, you have to find a number that both given numbers will divide into.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers