Question

1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =
The "n's" are supposed to be lower than the number

Answer 1

Is this asking for a sum? \[\Large \sum_{n=1}^N 4n(4n+2)= \]

Answer 2

seems very hard to understand where this question is going, and furthermore \(4_n(4_n+1)\) , does not yet make much sense, except you have some recursive formula and then it should most likely be \(a_n\)? but I might digress from the question itself.

Answer 3

@spacelimbus I don't see 4n(4n+2) is general form for the terms in sequence

Answer 4

probably this:
\[\Large \sum_{n=4}^{4n} n(n+2)=\sum_{n=4}^{4n}(n^2+2n) =\sum_{n=4}^{4n}n^2+2\sum_{n=4}^{4n}n\]

Answer 5

except the first term, 4*6,

Answer 6

Yes @Loser66 , I was paying too much attention to the last term of the given sum, however the above should fix this :) Only requires a shift of index and plugging in.

Answer 7

I think we have to wait for him to make it clear.

Answer 8

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.

Answer 9

sorry for the wait on me. i had to run out real quick

Answer 10

but there is no statement yet is there?

Answer 11

You should check and update the precise question again @seesawn, see the thing you have in your opening post is nothing but a mathematical expression, to use induction you would to have at least one closed form of this expression to which it is equal to.

If you don't have this, you can compute one on your own using summation. However, it would be a pointless task to use the summation method and then prove it again with induction, so I assume that you're question is missing something.

Answer 12

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =

thats my question

Answer 13

I am afraid I have to leave this open then, since this is not a question, you can see that for yourself that there is no right hand side next to the equal sign, which in fact makes it obsolete, they could have just written \(4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \dots + 4n(4n+2)\) as well with the same information.

Answer 14

the equation is supposed to look like this \[4_{n}(4_{n}+2)\]

Answer 15

Good, I am bereft of understanding this question :) I suggest to you to bump it to the top once in a while on OpenStudy and see if someone answers that understands it some more. Best luck!

Answer 16

thank you for trying!!!

Answer 17

your sequence should be something like this:
\[4\cdot 6 + 5\cdot 7 + 6\cdot 8 + \cdots + (4+n)(6 + n) \text{ where n starts at }0\]
i'm not sure what your \(4_n\) is supposed to mean.

Answer 18

im just showing it how i was shown it on the paper

Answer 19

as such, you could rewrite the terms as \(24 + 10n +n^2,n\in \mathbb{Z} \).

then the sum you could work from your formulas.
\[\sum_{i=0}^{n}\left(i^2+10i+24\right)=\sum_{i=0}^{n}i^2+\sum_{i=0}^{n}10i+\sum_{i=0}^{n}24=\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}+24(n+1)\]

Answer 20

the last term being 24(n+1). this is for n starting at 0.

Answer 21

i understand that what is shown on the paper, but it's quite useless unless you undersatnd what it means. I don't know what it means so it doesn't do me any good.

Answer 22

my math homework. i am just as confused as everyone that is trying to help me

Answer 23

no it isnt. its from pre calculus.
making up credits online

Answer 24

yes way. im a senior in high school, screwed off my sophmore year and have to make up the credit. im freaking confused

Answer 25

it's (4 times 6) plus (5 times 7) plus ..., yes?

Answer 26

idk, im going to try that and see if it works

Answer 27

hey

Answer 28

I can solve your question for ya

Answer 29

well you see if i were to write a couple of sums

Answer 30

and take differences of hte sums

Answer 31

the 3rd difference is constant and is =32

Answer 32

?

Answer 33

this means your solution is in the form
sum(x)=ax^3+bx^2+cx+d

Answer 34

you can just plug in for 4 different independant equations and solve your unknowns

Answer 35

or you can simplify it starting with the 32

Answer 36

24, 59, 107, 170, ... where are the differences the same?

Answer 37

the difference is the next term