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Prove this using this identity:

[tex]

k\binom{n}{k}=n\binom{n-1}{k-1}

[/tex]

[tex]

\binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}+....+(-1)

[/tex]

I was able to do this via differentiation, but not using this substitution. Any hints would be great.

[tex]

k\binom{n}{k}=n\binom{n-1}{k-1}

[/tex]

[tex]

\binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}+....+(-1)

^{n-1}\binom{n}{n}[/tex]

I was able to do this via differentiation, but not using this substitution. Any hints would be great.

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