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trasher [3.6K]
2 years ago
14

What is the sum of the first 5 terms of a geometric series with a sub 1 = 10 and r = 1/5?

Mathematics
2 answers:
Murrr4er [49]2 years ago
7 0

Answer:

12.496

Step-by-step explanation:

a=10 (first term)

r= 1/5 (common ratio)

sum of first five terms

s_{5} =  \frac{a( 1 -  {r}^{n} ) }{1- r}

=10{1-⅕⁵} ÷ 1-⅕

=10{1 - 1/3125} ÷ 4/5

=10{3124/3125} ÷ 4/5

=9.9968÷0.8

=12.496.

OR

a+ar+ar²+ar³+ar⁴

=10+(10x⅕)+(10x⅕²)+(10x⅕³)+(10x⅕⁴)

=10+2+0.4+0.08+0.016

=12+0.48+0.016

=12.496

Mice21 [21]2 years ago
5 0

Answer:

a 1 = 10

a 2 = 10 * 1/5 = 2

a 3 = 2 * 1/5 = 2/5

a 4 = 2/5 * 1/5 = 2/25

a 5 = 2/25 * 1/5 = 2/125

S 5 = a 1 + a 2 + a 3 +a 4 + a 5= 10 + 2 + 2/5 + 2/25 + 2/125 =

= 1250/125 + 250/125 + 50/125 + 10/125 + 2/125 = <u> 1562 / 125</u>

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Bas_tet [7]
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2 years ago
Use the binomial expansion and approximation to find √3​
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According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...

An acceptable result cannot be found manually for it requires a <em>high</em> number of elements, with the help of a solver we find that the <em>approximate</em> value of √3 is 1.732.  

<h3>How to approximate the value of a irrational number by binomial theorem</h3>

Binomial theorem offers a formula to find the <em>analytical</em> form of the power of a binomial of the form (a + b)ⁿ:

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Where:

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To learn more on binomial expansions: brainly.com/question/12249986

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8 0
1 year ago
Marty’s water bottle holds 4 cups of liquid. He has 24 fl oz of water to put into the bottle. Will all 24 fl oz fit in the bottl
alexgriva [62]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
If you can help please do! Thank you!
Aleks [24]

Answer:

see explanation

Step-by-step explanation:

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nadezda [96]
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