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3 years ago

How to solve the infinite series:

Mathematics

1 answer:

RoseWind [281]3 years ago

6 0

∞
∑3(1/4)ⁿ⁻¹ ==> replace n by consecutive values, starting with 1
ⁿ=¹
f(1) = 3(1/4)⁰ = 3 x 1 (any number raised to o is equal to 1
f(2) = 3(1/4)¹ = 3 x 1/4
f(3) = 3(1/4)² = 3 x (1/4)²
f(4) = 3(1/4)³ = 3 x (1/4)³
f(5) = 3(1/4)⁴ = 3 x (1/4)⁴
And so on and so forth. Then we have found a pattern that is:

f(n) = 3(1/4)ⁿ⁻¹
and with this you can find any number providing you know n

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The solution is p = $0.0001*q - $23

The general linear equation is:

p = m*q + c

Where m is the slope and c is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Here we have the two points:

price = $9, boxes = 320,000

price = $8.50, boxes = 270,000

We can rewrite these as:

(320,000 , $9)

(270,000 , $8.50)

Then the slope of the line will be:

$m = \frac{\$ 9 - \$ 8.50}{320,000 - 270,000} = \$ 0.00001$

Then the line is something like:

p = $0.0001*q + c

To find the value of c we can use one of the two given points, I will use the first one, (320,000 , $9).

Replacing that in our equation we get:

$9 = $0.0001*320,000 + c

$9 - $0.0001*320,000 = c = -$23

Then the linear equation is:

p = $0.0001*q - $23

If you want to learn more you can read:

brainly.com/question/11687874

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