Evaluate

100

å (100 – 2K)

K=5

thank u so much

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- Dec 3rd 2008, 06:15 PMSteph07I 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 PMskeeter
is this what you're trying to find?

$\displaystyle \sum_{k=5}^{100} (100-2k)$ - Dec 3rd 2008, 06:26 PMterr13
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 PMSteph07
thank u so much... you are wonderful!

- Dec 3rd 2008, 06:41 PMSoroban
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 PMSteph07
omg, thank u I was still workin on that one.. thank u so much