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3 years ago

Find the sum of the geometric series 1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}

Mathematics

1 answer:

Ainat [17]3 years ago

5 0

Answer:

S20 ≈ 4.942

Step-by-step explanation:

Sum of a geometric series is expressed as Sn = a(1-rⁿ)/1-r if r<1

a is the first term

r is the common ratio

n is the number of terms

Given the geometric series

1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}

Given a = 1,

r = 0.8/1 = 0.8²/0.8 = 0.8

n = 20 (The total number of terms in the series is 20)

Substituting this values in the formula above.

S20 = 1(1-0.8^20)/1-0.8

S20 = 1-0.01153/0.2

S20 = 0.9885/0.2

S20 ≈ 4.942

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Answer:

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Step-by-step explanation:

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prisoha [69]

<h3>Given:</h3>

h= 19 ft
r= 12 ft

h= Height
r= Radius

The volume of the given cone.

<h3>Solution:</h3>

$\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}$

$\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}$

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Substitute the values according to the formula.

$V=\frac{1}{3}×3.14×{12}^{2}×19$

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2 years ago

Brainliest for the correct answer!

liraira [26]

Answer:

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Step-by-step explanation:

>First find the equation of function A

general equation of a line is y=mx+b

m = (y2-y1)/(x2-x1)= (0-(7/2))/(-7-0) = (-7/2) *(1/-7) = 1/2

consider the point (-7,0)

0 = -7(1/2) +b

7/2 = b

Function A has the equation y= (1/2)x +7/2

>rewrite the equations to fit the standard form

y-3 = (1/4)x ; add 3 to both sides

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y= -x + 7/2

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> intercept less than A

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y-intercept for function y= (1/4) x +3 is 3

3 < 7/2, so the answer is y-3 = (1/4)x

> intercept equal to A

y-intercept for function A , y= (1/2)x +7/2, is 7/2

y-intercept for function y= -x + 7/2 is 7/2

7/2=7/2 , so the answer is 4y = -4x +14

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y-intercept for function A , y= (1/2)x +7/2, is 7/2 =3.5

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