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I'm having some issues solving some apparently 'basic' summation problems where they give you a couple summations and you derive the missing summation.

I would appreciate any help not only solving this particular question but actually understanding the situation.

Thanks!

1. The problem statement, all variables and given/known data

Suppose:

113

[tex]\Sigma[/tex] a_{k}= 641

k=9

and

507

[tex]\Sigma[/tex] a_{k}= 2091

k=70

and

113

[tex]\Sigma[/tex] a_{k}= 130

k=70

Then:

507

[tex]\Sigma[/tex] a_{k}= ?

k=114

2. Relevant equations

I think everything relevant is provided above.

3. The attempt at a solution

I have absolutely no idea how to start. I've googled summation problems and read quite a bit more than what is in my text. I keep finding information on what I can already do; problems like:

10

[tex]\Sigma[/tex] a-20 = ?

k=1

Where a is a constant instead of having the 'k' subscript so you can take (10-(1-1)) * (a-20).

Although, for some reason sticking the subscript onto a throws me off completely. Any suggestions are welcome.

Thank you for your time!

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# Some basic summation problems

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