# I dont even know what to title this... help please :(

• Dec 3rd 2008, 06:15 PM
Steph07
I dont even know what to title this... help please :(
Evaluate
100
å (100 – 2K)
K=5

thank u so much
• Dec 3rd 2008, 06:24 PM
skeeter
is this what you're trying to find?

$\displaystyle \sum_{k=5}^{100} (100-2k)$
• Dec 3rd 2008, 06:26 PM
terr13
You can pull out the 100 from the equation, and have
$\displaystyle 9600 - \sum_{k=5}^{100} 2k$
Now you can pull our the 2 from the summation
$\displaystyle 9600-2(\sum_{k=5}^{100} k)$
Now simply solve that summation, which should be easy.
• Dec 3rd 2008, 06:35 PM
Steph07
thank u so much... you are wonderful!
• Dec 3rd 2008, 06:41 PM
Soroban
Hello, Steph07!

Quote:

Evaluate: .$\displaystyle \sum^{100}_{k=5}(100-2k)$

We have: .$\displaystyle S \;=\;90 + 88 + 86 + \hdots - 96 - 98 - 100$

This is an arithmetic series with:
. . first term $\displaystyle a = 90$, common difference $\displaystyle d = -2$, and $\displaystyle n = 146$ terms.

The sum is: .$\displaystyle S \;=\;\frac{n}{2}\bigg[2a + (n-1)d\bigg] \;=\;\frac{146}{2}\bigg[2(90) + 145(-2)\bigg] \;=\;\boxed{-8030}$

• Dec 3rd 2008, 06:44 PM
Steph07
omg, thank u I was still workin on that one.. thank u so much