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Bond [772]
3 years ago
7

give an example of a convergent infinite series whose sum equal 3/5. explain how you know your series converges and write out wo

rk to show that its sum is in fact 3/5
Mathematics
1 answer:
krek1111 [17]3 years ago
5 0

Answer:

The series 1/5, 2/15, 4/45, 8/135... converges and sums up to 3/5

Step-by-step explanation:

Consider the infinite geometric series

1/5, 2/15, 4/45, 8/135...

With first term, a=1/5

common ratio, r = ⅔

The series converge because the common ratio, |r|<1.

The sum to infinity of a geometric series, S= a/(1-r)

S= 1/5 ÷ (1-⅔) = 1/5 ÷ 1/3 = 3/5

Therefore, the geometric series 1/5, 2/15, 4/45, 8/135... sums up to 3/5.

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16 - 6 into 2 + 3 by 23 - 3 into 2 ​
Alinara [238K]

Answer:

80.5

Step-by-step explanation:

8 0
3 years ago
Find the cube roots of 8(cos 216° + i sin 216°).
Tomtit [17]
z^3=8(\cos216^\circ+i\sin216^\circ)
z^3=2^3(\cos(6^3)^\circ+i\sin(6^3)^\circ)
\implies z=8^{1/3}\left(\cos\left(\dfrac{216+360k}3\right)^\circ+i\sin\left(\dfrac{216+360k}3\right)^\circ\right)

where k=0,1,2. So the third roots are

z=\begin{cases}2(\cos72^\circ+i\sin72^\circ)\\2(\cos192^\circ+i\sin192^\circ)\\2(\cos312^\circ+i\sin312^\circ)\end{cases}
5 0
3 years ago
Trigonometry is hard someone help<br> Please :)
vlada-n [284]
<h3>Answer:  Approximately 35.54 degrees</h3>

=============================================================

Explanation:

With respect to reference angle x, the 5 is the opposite side, and the adjacent side is 7 units long.

We'll use the tangent ratio here

tan(angle) = opposite/adjacent

tan(x) = 5/7

x = arctan(5/7)

x = 35.5376777919743 approximately

x = 35.54

I rounded to two decimal places, but you can round however you need to or however your teacher instructs. Arctangent is the same as inverse tangent. Be sure that your calculator is in degree mode.

7 0
3 years ago
Compare and Contrast a square and an equilateral triangle? Be sure to communicate and discuss using mathematical language, ideas
ella [17]

The <u>comparison</u> and <u>contrast</u> between a square and an <em>equilateral triangle</em> are stated and explained below:

What is a <u>square</u>? A <u>square</u> is a <em>plane shape</em> with an equal length of sides. This implies that the <em>measure</em> of its length is the same as that of its <u>breadth</u>.

What is an equilateral triangle? A <em>triangle</em> is a <em>plane shape</em> with<u> three </u>sides, and a <em>sum </em>of its <u>internal</u> angles to equal 180^{o}. Thus an <em>equilateral triangle </em>is a type of triangle with <em>equal lengths of sides</em>, and therefore equal internal angles.

<u>Comparison</u>: i. The two shapes have <em>equal lengths</em> of sides.

ii. An equilateral triangle and a square are examples of <u>plane shapes</u>.

<u>Contrast</u>: i. An equilateral triangle has<em> three sides</em>, while a square has <em>four sides</em>.

ii. An equilateral triangle has <em>three internal angles</em>, while a square has <em>four internal angles</em> which are right angles.

iii. The sum of <u>internal </u>angles of an equilateral triangle is 180^{o}, while that of a square is 360^{o}.

For more clarifications on the properties of squares and triangles, visit:

brainly.com/question/12410856

#SPJ1

Kindly get 1-on-1 help from an expert tutor for more explanations if required.

6 0
2 years ago
Can someone pls help me solve this? <br> 7&lt;2m-23
gregori [183]
7 < 2m - 23
add 23 to both sides
30 < 2m
divide both sides by 2
15 < m
same as m > 15
8 0
3 years ago
Read 2 more answers
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