Question

Use mathematical induction to prove the statement is true for all positive integers n.

The integer n3 + 2n is divisible by 3 for every positive integer n.
PLEASE HELP I GIVE MEDALS PLEASE HELP

Answer 1

1. for n=1 statement is true, we can check it: 1+2=3 => 3 divides 3
2. Assume that the statement is true for n=k: 3 divides k^3+2k
3. Then it has to be right for n=k+1 - let's check
(k+1)^3+2(k+1)=k^3+3k^2+5k+3=(k^3+2k) + (3k^2+3k+3) = (k^3+2k) + 3(k^2+k+1) - we can divide this by 3, so the statement is proved

Answer 2

Is that how id answer the question fully? @wintry

Answer 3

how would I answer this one as it is?

Answer 4

I don't know your requirements, this is how i was taught to solve this type of problems...

Answer 5

I dont get what to do in the question ? @wintry

Answer 6

Do you know what is math. induction?

Answer 7

I got it .... can you help with:
A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.
Help explaining

Answer 8

@wintry

Answer 9

Well, it's easy one.
H(n) - is the sequence of heights of the tree every week, n is the number of weeks
H(n)=5+0.038*n

Answer 10

Sorry, it's in meters
I'll rewrite it in cm: H(n)=500+3.8*n

Answer 11

why 500 @wintry

Answer 12

because 5 meters = 500 cm, you cannot add meters and cm, you should work in only system of measurements (I'm not sure whether I explain it correctly, English is not my native language)

Answer 13

you explain fine

Answer 14

is H(n)=500+3.8*n the answer or is there a different answer @wintry

Answer 15

It has to be the answer, if I've got the problem correctly

Answer 16

I also have trouble with these two @wintry

Answer 17

just the options I thought the second one was B but Im not sure

Answer 18

B is in the first, and I'm not sure about the second one. It has to be A, but it might be D cause I'm not sure whether this sequence ends on 81 or continues. If it continues infinitely the answer is D

Answer 19

I think it ends at 81 because it doesnt have "..." i think @wintry

Answer 20

so A?

Answer 21

I think so too
Yes, A

Answer 22

Do you mind If I discuss a couple more Im not sure about thats it ?

Answer 23

@wintry

Answer 24

I don't, post here :-)

Answer 25

Youre Awesome ..
the first is Find the first six terms of the sequence.

a1 = -6, an = 4 • an-1
Options are:
0, 4, -24, -20, -16, -12

-24, -96, -384, -1536, -6144, -24,576

-6, -24, -20, -16, -12, -8

-6, -24, -96, -384, -1536, -6144

Answer 26

the last two are :
THANKS :)

Answer 27

Obviously, it's C or D because of -6 in the first place.
a2=-24, a3=-96, so it's D

Answer 28

thats what I was thinking because i did the -6*4 and what about the next two?

Answer 29

The second is B. Should I explain why? If you can use a calculator, you can just plug in numbers in formulae and find the right one this way

Answer 30

the Determine whether the sequence converges or diverges. If it converges, give the limit.
one is B? and my calculator broke this week :(

Answer 31

No, arithmetic sequence, -579+42(n-1)

Answer 32

what about the one under it
?

Answer 33

The last one seems to be B

Answer 34

wait, I need to think a little bit about this one

Answer 35

okay no problem

Answer 36

We can find the sequence itself

Answer 37

It will be \[\frac{ 288 }{ 6^{n}}\]

Answer 38

so A?

Answer 39

No, why? It's zero, of course

Answer 40

\[\lim_{n \rightarrow \infty}\frac{ 288 }{ 6^{n} }=0\]

Answer 41

oh sorry about that that means the answer is B right ?

Answer 42

Yes

Answer 43

thank you so much

Answer 44

you are welcome