# Thread: Can someone help me understand how to evaluate sums?

1. ## Can someone help me understand how to evaluate sums?

Hello,
I was just wondering if someone can help me understand how to go about evaluating sums???

I am very new and lost as to how to get started... I don't understand the idea behind it....

For example:
2n
E i
i=5

2. $\sum\limits_{i = 1}^{2n} i = \frac{{2n\left( {2n + 1} \right)}}{2} = n\left( {2n + 1} \right)$
And
$\sum\limits_{i = 5}^{2n} i = \sum\limits_{i = 1}^{2n} i - \sum\limits_{i = 1}^4 i$

So?

I don't really understand what each step is suppose to accomplish but....

But, trying to draw from your example, is this correct?
[2n(2n+1)+2n(2n+2)+2n(2n+3)+2n(2n+4)+2n(2n+5)]/2 ?????????? and the result is 25??

Thanks again!

4. Originally Posted by matthayzon89
I don't really understand what each step is suppose to accomplish but....But, trying to draw from your example, is this correct?
[2n(2n+1)+2n(2n+2)+2n(2n+3)+2n(2n+4)+2n(2n+5)]/2 ?????????? and the result is 25??
The answer is $\sum\limits_{i = 5}^{2n} i = n\left( {2n + 1} \right) - 10 = 2n^2 + n - 10$

5. Where did the -10 come from?

Since this is finite sum evaluation couldn't I evaluate it to a specific number?

Thanks

6. Originally Posted by matthayzon89
Where did the -10 come from?
$\sum\limits_{i = 1}^4 i = 10$

7. Can someone help me understand what N is worth here? do I just count n as 1? or what?

4n
E(n^3)i
i=0

8. Originally Posted by matthayzon89
Can someone help me understand what N is worth here? do I just count n as 1? or what?
4n
E(n^3)i
i=0
I don't think you will understand this but here goes:
$\sum\limits_{i = 0}^{4n} {n^3 i} = n^3 \sum\limits_{i = 0}^{4n} i = n^3 \left( {\frac{{4n\left( {4n + 1} \right)}}
{2}} \right) = n^3 \left( {2n(4n + 1)} \right)$

9. In the expression $\sum\limits_{i = 0}^{4n} {n^3 i}$, $n$ is unknown. This is the sum $n^3\cdot 0+n^3\cdot 1+n^3\cdot2+\dots+n^3\cdot4n$ with $4n+1$ terms. Until the value of $n$ is given, it cannot be evaluated to a number.