Question

Can someone tech me how to do this please? It's confusing
What is the partial sum of ?
25 on top of the E, i=10 on bottom, and -2-8i on the side

Answer 1

Do you have any selections?

Answer 2

Answers? Then yes
2208
-2272
2272
-2208

Answer 3

\[\large \sum_{i=10}^{25}(-2-8i)=\sum_{i=10}^{25}(-2)-8\sum_{i=10}^{25}i \]
Are you familiar with the formula:
\[\large \sum_{i=1}^{n}i =\frac{n(n+1)}{2}\]

Answer 4

What do you think the answer is?

Answer 5

Yep I'm familiar with the formula, I just wasn't sure where everything goes

Answer 6

And I'm not sure what the answer is

Answer 7

Ok, you can use that formula on the second sum, but you have to "modify" it. Notice that the formula starts at i=1, but your sum starts at i=10. So, to transform that sum in such a way that you can use the formula, you can make use of this "identity"
\[\large \sum_{i=10}^{25}i=\sum_{i=1}^{25}i-\sum_{i=1}^{9}i \]
The first sum on the right side is summing the terms from 1 to 25:
1, 2, 3, ..., 9, 10, ... 25
But then you subtract off the terms from 1 to 9 to just get the terms from 10 to 25

And both sums start with the index i=1, so you can use the formula on both of those summations

Answer 8

So if my sum was 5 for example, then it would change to 20 on the top?

Answer 9

No wait, sorry im just stuck on this identity concept, are there more than one identity?

Answer 10

Let me try to illustrate: