Question

Evaluate the summation of negative 2 n minus 3, from n equals 2 to 10..

Answer 1

\[\sum_{2}^{10}(2n-3)\]

Answer 2

Is that the correct formula?

Answer 3

\[\sum_{n=2}^{10}-2n-3\]

Answer 4

whoops

Answer 5

The big Greek letter Sigma is the mathematically symbol for inserting the n value into the function at the right and adding it to the previous answer to get the total answer from a to b.

Answer 6

Do you understand that?

Answer 7

Yes

Answer 8

Okay, So now you evaluate the sigma function beginning at 2 to 10. those will be the a and b's.

Answer 9

I know there's a simpler equation for solving it, I just dont remember what it is or what goes where in that equation. If you could give me that, it would be much help.

Answer 10

You are correct there is.

Answer 11

I will insert them here.
\[\sum_{k=1}^{n}k=\frac{ n(n+1) }{ 2 }\]

Answer 12

Okay now I'm confused as to how I would use that to solve it.

Answer 13

Wait there's more fancier equations.

Answer 14

There are certain rules and properties of sigma notations.
One is the addition or subtraction. There is another for constants. Another for variables raised to powers.

Answer 15

\[\sum_{k=1}^{n}c=cn\]
\[\sum_{i=1}^{n}i=\frac{ n(n+1 }{ 2 }\]
\[\sum_{i=i_{a}}^{n}(a _{i \pm b _{i}})=\sum_{i=i _{a}}^{n}a _{i}\pm \sum_{i=_{a}}^{n}b _{i}\]

Answer 16

You have a constant sigma notation INSIDE an subtraction sigma notation.

Answer 17

Okay?

Answer 18

Okay so?

Answer 19

You are allowed to first break up the problem using the addition subtraction property. From there you have a constant sigma notation and the rest subtraction sigma notation. Correct?

Answer 20

Yeah, so what then?

Answer 21

So you then have :
\[-2\sum_{n=2}^{10}n-\sum_{n=2}^{10}3\]

Answer 22

You see how I got that?

Answer 23

Yeah. You used the last one, a being -2 and b being -3.

Answer 24

Now, wait. a and b are the limits. such like the bottom and the top.

Answer 25

Okay? What does that mean then

Answer 26

So now you can evaluate your problem, a little easier I guess.

Answer 27

Notice the right hand side is a constant of 3. Correct?

Answer 28

Yes

Answer 29

So what property is that, I listed it above somewhere.

Answer 30

You said there is one for constants, so would that be it?

Answer 31

correct.

Answer 32

Now notice the left hand side has a single variable with the constant removed to the outside.

Answer 33

Yes

Answer 34

Now this is basically evaluation from here on out.

Answer 35

Yes?

Answer 36

Right?

Answer 37

\[\sum_{n=2}^{10}i=\frac{ n(n+1) }{ 2 }\]
You use that for the left hand side. then you multiply by negative 2.

Answer 38

and then you use :
\[\sum_{i=1}^{n}c=cn\]
for the right side and subtract the first from this answer to get your final answer.

Answer 39

I used the textbook variables, so you can switch i to n and c to your constant.

Answer 40

The answer I got with that is -135.

Answer 41

That is correct, you used the formulas above?

Answer 42

Yeah, thanks so much. :)

Answer 43

Not at all, I hope I helped you out.

In my opinion I would just have inserted each number into the function and written down the answer and gone to the next number and repeated and at the end jsut added or subtracted whatever to get my answer.

Answer 44

But I guess you can say that this makes it easier to look at the numbers in some ways.

Answer 45

I like it better if there's an equation to just insert numbers rather than take the long way. But thanks for the help. :)

Answer 46

No problem,

Answer 47

I hope I really did help you out, as I wont be able to help you on test day :).