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## Homework Statement

How to use binomial theorem for finding sums with binomial coefficients?

Example: [tex]S={n\choose 1}-3{n\choose 3}+9{n\choose 5}-...[/tex]

How to represent this sum using [itex]\sum\limits[/itex] notation (with binomial theorem)?

## Homework Equations

[itex](a+b)^n=\sum\limits_{k=0}^{n}{n\choose k}a^{n-k}b^k[/itex]

## The Attempt at a Solution

I am completely stuck on this types of problems (modify binomial formula so that it gives some arbitrary sum). Could someone please explain this example?