**Exercise 3.** Give a combinatorial proof that\[\sum_{k=1}^{n} k \binom{n}{k} = n 2^{n-1}.\]*Hint:* Consider selection of a committee and chairperson.

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Description: **Exercise 3.** Give a combinatorial proof that\[\sum_{k=1}^{n} k \binom{n}{k} = n 2^{n-1}.\]*Hint:* Consider selection of a committee and chairperson.

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Math

Advanced Math

Exercise 3. Give a combinatorial proof that = n2"-1 k Hint: Consider selection of a committee and chairperson.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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**Exercise 3.** Give a combinatorial proof that

\[
\sum_{k=1}^{n} k \binom{n}{k} = n 2^{n-1}.
\]

*Hint:* Consider selection of a committee and chairperson.

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