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
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.
all right great thank you so much!
You're welcome!
To find the sum of the given expression, we need to evaluate the expression for each value of k within the specified range (from k = 1 to k = 12) and then add up the results.
The expression is (10k - 8)(6k + 7) and we are summing this expression as k varies from 1 to 12.
To simplify the process, we can expand the given expression and then sum up the terms.
1. First, we need to substitute each value of k into the expression (10k - 8)(6k + 7):
For k = 1: (10(1) - 8)(6(1) + 7) = (2)(13) = 26
For k = 2: (10(2) - 8)(6(2) + 7) = (12)(19) = 228
For k = 3: (10(3) - 8)(6(3) + 7) = (22)(25) = 550
Continue this process until k = 12.
2. Now, we have a list of values obtained by evaluating the expression for each value of k. We need to add these values together to find the sum.
Sum = 26 + 228 + 550 + ... (add the values obtained for each k from 1 to 12)
3. Finally, perform the addition to find the sum.
Keep in mind that using mathematical software or calculators can simplify this process, especially for longer series, by automatically performing the calculations and providing the final sum.