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Mathematics 17 Online
OpenStudy (anonymous):

on this one i just need to know how to set it up...

OpenStudy (anonymous):

\[\sum_{k=1}^{50}[(k+1)^2-k^2]\]

OpenStudy (anonymous):

i'll solve it if i can just get help setting it up...

OpenStudy (anonymous):

your first step is to simplify the equation: (k+1)(k+1) - k^2 (multiply it all out) what do you get?

OpenStudy (anonymous):

2k+1

OpenStudy (anonymous):

great! so now it's a much easier problem. and you'll do it just like the last problem you did.

OpenStudy (anonymous):

the sum of a constant is just that constant right?

OpenStudy (jamesj):

\[ \sum_{j=1}^n c = nc \]

OpenStudy (anonymous):

so my final answer is.... 2600

OpenStudy (jamesj):

Yes

OpenStudy (anonymous):

SWEET!!!!

OpenStudy (jamesj):

\[ \sum_{k=1}^{50} (2k+1) = 2 \sum_{k=1}^{50} k + \sum_{k=1}^{50} 1 = 2 \frac{50(50+1)}{2} + 50 = 2550 + 50 = 2600. \]

OpenStudy (anonymous):

that is exactly what i did

OpenStudy (jamesj):

good

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