All categories

3 years ago

((Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Mathematics

1 answer:

Lina20 [59]3 years ago

5 0

Answer:

Step-by-step explanation:

A series is said to be convergent if |r| < 1. Where r is the common ratio of the series.

If |r| ≥ 1 then the geometric series diverges.

12/5 + 48/25 + 192/125 + ....

r = 192/125 ÷ 48/25 = 4/5

r = 48/25 ÷ 12/5 = 4/5

In the series, r is less than 1. So the series is convergent.

You might be interested in

When Frank buys three packs of pens, he knows he has 36 pens. When he buys five packs, he knows he has 60 pens. What is the cons

jenyasd209 [6]

Answer:

Loggerhead turtles live and migrate around the Atlantic Ocean. Which of the following is an adaptation of Loggerhead turtles? *

Step-by-step explanation:

hi sup

7 0

2 years ago

Read 2 more answers

What's the pattern of 160,80,40,20,10

Brrunno [24]

The pattern is that each number is decreasing by half

3 0

3 years ago

Read 2 more answers

Y = 3x + 2<br> What is x?

Aliun [14]

That question is impossible because we don’t know what we are trying to solve for it has to be x or y in this scenario it can’t be both we need one to find the other

4 0

2 years ago

Read 2 more answers

What should you do first to simplify the expression ( 54 + 6) ÷ 26 + 5?

TiliK225 [7]

Do the brackets first as it says in BIDMAS

7 0

2 years ago

Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .

anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

We need to begin with the definition of tangent:

$tan (x) =\frac{sin(x)}{cos(x)}$

So we can replace into our formula and we got:

$tan(x-y) = \frac{sin(x-y)}{cos(x-y)}$ (1)

We have the following identities useful for this case:

$sin(a-b) = sin(a) cos(b) - sin(b) cos(a)$

$cos(a-b) = cos(a) cos(b) + sin (a) sin(b)$

If we apply the identities into our equation (1) we got:

$tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}$ (2)

Now we can divide the numerator and denominato from expression (2) by $\frac{1}{cos(x) cos(y)}$ and we got this:

$tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}$

And simplifying we got:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

And this identity is satisfied for all:

$(x-y) \neq \frac{\pi}{2} +n\pi$

8 0

2 years ago