math Algebra 2
posted by Anonymous on .
I have absolutely no idea how to do this please help!
Find the sum:
it has the sigma sign with 12 at the top, (10k8)(6k+7) in the middle and k=1 at the bottom

It just means, add:
the value of (10k8)(6k+7) when k=1
plus
the value of (10k8)(6k+7) when k=2
plus
the value of (10k8)(6k+7) when k=3
plus
... (and so on, 4, 5, to 9, 10)...
the value of (10k8)(6k+7) when k=11
plus
the value of (10k8)(6k+7) when k=12
So you could just do it by calcuating out:
the value of (10k8)(6k+7) when k=1 is 26
plus
the value of (10k8)(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 shortcuts.
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. 
all right great thank you so much!

You're welcome!