Question

I have absolutely no idea how to do this please help!
Find the sum:
it has the sigma sign with 12 at the top, (10k-8)(6k+7) in the middle and k=1 at the bottom

Answer 1

It just means, add:

the value of (10k-8)(6k+7) when k=1
plus
the value of (10k-8)(6k+7) when k=2
plus
the value of (10k-8)(6k+7) when k=3
plus
... (and so on, 4, 5, to 9, 10)...
the value of (10k-8)(6k+7) when k=11
plus
the value of (10k-8)(6k+7) when k=12

So you could just do it by calcuating out:

the value of (10k-8)(6k+7) when k=1 is 26
plus
the value of (10k-8)(6k+7) when k=2 is 228

and so on.

It mightn't be a bad idea to do that anyway, since you will understand it thoroughly and be sure of your answer.

However, there are short-cuts.

It may be that you've already covered these in your class, or it may be that you were given this exercise so that you'll appreciate them when you do cover them! :-)

There is a formula for the sum of x from 0 to n and a formula for the sum of x^2 from 0 to n. You can probably find them in your text.

By multiplying out the expression, we can then use those formulas.

Answer 2

all right great thank you so much!

Answer 3

You're welcome!