Identify whether these series are divergent or convergent geometric series and find the sum, if possible.

Answers

Answer 1

Answer: A geometric series:
$\sum^(\infty)_(i=1)=a_1 * r^(i-1)$
It's convergent if |r|<1.
It's divergent if |r|≥1.
The sum can be found if it's a convergent series; it's equal to $(a_1)/(1-r)$ .

3.
$\sum^(\infty)_(i=1) 12 ((3)/(5))^(i-1) \n \na_1=12 \nr=(3)/(5) \n \n|r|<1 \hbox{ so it's convergent} \n \n\sum^(\infty)_(i=1) 12 ((3)/(5))^(i-1)=(12)/(1-(3)/(5))=(12)/((5)/(5)-(3)/(5))=(12)/((2)/(5))=12 * (5)/(2)=6 * 5=30$

The answer is: This is a convergent geometric series. The sum is 30.

4.
$\sum^(\infty)_(i=1) 15(4)^(i-1) \n \n a_1=15 \n r=4 \n \n |r| \geq 1 \hbox{ so it's divergent}$

The answer is: This is a divergent geometric series. The sum cannot be found.

Related Questions

Please answer all three questions for full points.
Solve the following equation by transforming it into a perfect square trinomial.* 3x2 + 12x = 63
A rectangular field is 280 m by 390 m. A rectangular barn 25 m by 33 m is built in the field. How much area is left over?
Help with question 9 please
A local drive-in theatre sells entrance tickets for cars on weekend nights. At capacity , the drive in can hold 72 cars. The function c(n)=25n represents the drive-ins revenue on a weekend night, where n represents the number of cars. In this situation, what is the domain of C(n)?

this is part 2 and you just have to find the total area in sq ft and also answer how much material do you need to make 3 backpacks

Answers

1. 1 1/8= 18/16

5/16*2= 10/16

4/16*2= 8/16

9/16= 9/16

1/2= 8/16

18/16 + 10/16 + 8/16 + 9/16 + 8/16= 53/16

Simplify:

4 & 5/16sq ft

2. All you do is multiply that by 3... so 4 & 5/16 = 53/16 53/16*3 = 159/16 = 9 & 15/16 sq ft

Christina is making a blanket for her baby granddaughter. The blanket will have ribbon around all 4 edges. There will be:94 feet of ribbon on the top edge94 feet of ribbon on the bottom edge134 feet of ribbon on the left edge134 feet of ribbon on the right edgeHow much ribbon will Christina need to make the blanket?

Answers

94+94+134+134=188+268=200+246=446

94+94=188
134+134=268
188+268=456
Your answer would be 456

ok the 100 point question is... if i am walking to work at 6:00 and it takes me three hours to get there, and jimmy walks to the same place of work two hours later at 8:00 walking two mph faster than me, what time did i get to work?

Answers

9:00 tricky question also

ok so at 6:00, you start walking. It takes me 3 hours to get there
6+3=9
you got there at 9:00
no idea what the jimmy buisieness is

If 160 is divided by x, then the remainder is 4. What is the remainder when 315 is divided by x?

Answers

Let us rewrite this equation as:
160/x = some number + 4/x
we can assume that some number of x's can fit into 160, but x is greater than 4 so we have a remainder.
We can figure out by using the remainder that x is completely divisible into (160-4) or 156. Knowing this we can assume that x is some factor of 156 that is greater than 4.
Let us list the factors of 156
1,2,3,4,6,12,13,26,39,52,78,156
Now let us refer back to the restrictions we put on x.
x must be > 4 as anything less than 4 would divide at least 1 more time into it. So now we are left with a bunch of other factors. And the cool thing is that all of the factors excluding anything that is = or < 4 all work for getting a remainder of 4. Thus we can use the largest factor and set it equal to x.
So x = 156
then if we divide 315 by x or 315/x = 315/156 = 2 and a remainder of 3
so the answer would be 3.

How do you multiply 5/12 times 2/9?

Answers

$(5)/(12)\cdot(2)/(9)=(5)/(6)\cdot(1)/(9)=(5)/(54)$

Ann can buy either a pair of jeans or shoes with the allowance she saved up. What is the opportunity cost if she buys the jeans?

Answers

The opportunity cost that Ann is going to have if she buys the pair of jeans is the chance to buy the pair of shoes with her allowance. She exchanged her opportunity of buying the shoes by buying the pair of jeans. This is the opportunity cost because the potential of losing the alternative (shoes) happened by purchasing the other.

Answer:

plato answer is A; getting a new pair of shoes

Step-by-step explanation:

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I need help please help

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Pls helpPls help Pls gelp