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3 years ago

Why does this series converge? ∞ ∑ (n+1)/[(n)(n+2)(n+3)] n=1

Mathematics

1 answer:

ollegr [7]3 years ago

6 0

Compare the series to the convergent series,

$\displaystyle\sum_{n=1}^\infty\frac1{n^2}$

By the limit comparison test, the given series converges because

$\displaystyle\lim_{n\to\infty}\frac{\frac{n+1}{n(n+2)(n+3)}}{\frac1{n^2}}=\lim_{n\to\infty}\frac{n(n+1)}{(n+2)(n+3)}=1$

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Ann bought 4 souvenirs during 2 days of vacation. How many days will ann have to spend on vacation before she will have bought a

Anna007 [38]

Answer: She will have to spend 8 days on vacation before she will have bought a total of 16 souvenirs.

Step-by-step explanation:

Given: Ann bought 4 souvenirs during 2 days of vacation.

Per day she buys = $\dfrac{4}{2}=2$ souvenirs [unit rate]

To buy 16 souvenirs , she will take $\dfrac{16}{2}$ = 8 days.

Hence, she will have to spend 8 days on vacation before she will have bought a total of 16 souvenirs.

7 0

3 years ago

Pls help

mafiozo [28]

Answer:

18 minutes to run a mile

Step-by-step explanation:

1.5 is equal to 150%. so given that you have 12 minutes you can do what is 150% to 12 so 100% of 12 is 12 and 50% of 12 is 6 and 6 + 12 is 18

8 0

3 years ago

Please help me with this

Cerrena [4.2K]

Answer:

Yes;Each side of triangle PQR is the same length as the corresponding side of triangle STU

Step-by-step explanation:

You can observe the sides of both triangles to see if this property holds

Lets check the length of AB

A(0,3) and B(0,-1)

$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\\\AB=\sqrt{(0-0)^2+(-1-3)^2} \\\\\\\\AB=\sqrt{0^2+-4^2} \\\\\\AB=\sqrt{16} =4units$

Now check the length of the corresponding side DE

D(1,2) and E(1,-2)

$DE=\sqrt{(1-1)^2+(-2-2)^2} \\\\\\DE=\sqrt{0^2+-4^2} \\\\\\DE=\sqrt{16} =4units$

The side AB has the same length as side DE.This is also true for the remaining corresponding sides.

6 0

4 years ago

Translate each verbal description into an algebraic expression. Simplify the expression when you can

REY [17]

Hello there!
So, let's start off with the first one:

A) 60% of One - half x

I believe a couple of possible equations would be: 0.60*1/2x or 0.60*0.5x. 1/2 and 0.5 both equal half of a number. The 0.60 would equal 60%. I'll plug 10 into x of both equations to see what I come up with:

First Equation:
1/2 * 10/1 = 10/2 or 5.
0.60 * 5 = 3

Second Equation:
0.5 * 10 = 5
0.60 * 5 = 3

So they both come up with the same answer, so that makes them both equal, which makes them both possible equations.

B) 7 times z reduced by a third of the product

7z - 1/3 seems like a good equation. Let me plug in 5 for z to solve:

7 * 5 = 35
Convert 35/1 into 105/3 by multiplying both sides by 3
105/3 - 1/3 = 104/3 (approx. 34.7)

C) Three-fourths of V subtracted from 6 times two-ninths

A good equation for this would probably be (6*2/9)-3/4v. I'll plug 5 into v to show how we would solve the equation:

6/1 * 2/9 = 12/9 or 1 1/3.
3/4 * 5/1 = 15/4 or 3 3/4.
(Use the fractions 16/12 and 45/12 as 16/12 = 12/9 and 15/4 = 45/12)
16/12 - 45/12 = -29/12 or −2 5/12

D) Sum of 2x, (2/3 + 5) and 11-x

I think the right equation for this would be 2x + (2/3 + 5) + 11-x. Plug in 3 for x to solve:

(Use 15/3 when adding 2/3 and 5 because 5 = 15/3)
2/3 + 15/3 = 17/3 or 5 2/3
2 * 3 = 6
11 - 3 = 8
(Use 18/3 and 24/3 when adding up 6 + 5 2/3 + 8 as 6 = 18/3 and 8 = 24/3
17/3 + 18/3 + 24/3 = 59/3 or 19 2/3

Sorry if this confused you xD but, basically, the possible equations are as follows:

1 = 0.60*1/2x or 0.60*0.5x
2 = 7z - 1/3
3 = (6*2/9)-3/4v
4 = 2x + (2/3 + 5) + 11-x

I hope this helped! If not, I'm very sorry. Algebra isn't my strong suit ^.^'

3 0

3 years ago

Helppp I really don't understand full explanation would be nice, please.

Dafna1 [17]

Step-by-step explanation:

y = mx + b.

y = -5/x -5

I hope this helps,

8 0

3 years ago