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kipiarov [429]
3 years ago
12

I need help with the bottom part I know the top parr

Mathematics
1 answer:
Inessa05 [86]3 years ago
7 0
You used distributive property because when there’s parentheses in a equation you need to distribute the number outside of the parentheses
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Which of the following geometric series converges?
Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}

Multiply both sides by <em>r</em> :

rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n

Subtract the latter sum from the first, which eliminates all but the first and last terms:

S_n-rS_n=a-ar^n

Solve for S_n:

(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}

Then as gets arbitrarily large, the term r^n will converge to 0, leaving us with

S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0
3 years ago
Dr. Keller has a bookcase in her office with three shelves each shelf has the same number of books on it there are 23 books on t
KiRa [710]

Answer:

69

Step-by-step explanation:

23 on each shelf x 3 shelves = 69 books

7 0
2 years ago
Why does the pressure go down when the velocity of a fluid increase?<br> Please help asap!
Hunter-Best [27]

Answer:It is the conversion of one form of energy to another. If a fluid flow is restricted, the velocity of the fluid reduces, thereby the kinetic energy decreases and the equivalent amount of energy is increased as the pressure energy, which therefore increases the point pressure of the fluid.

Step-by-step explanation:

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2 years ago
9y2 and 9y<br><br> like terms or unlike terms
Alinara [238K]

Answer:

unlike terms

Step-by-step explanation:

since the first 9y is squared they cannot be combined since the other isn't squared, they cannot be simplified, nor are they alike

5 0
3 years ago
it is not always helpfule to rewrite an equation in standard form as a first step in solving it? true or false
Anni [7]

Answer:

True

Step-by-step explanation:

8 0
3 years ago
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