Question

Prove that $\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$

score 22.8k · Answer 1 · 2014-04-13 20:10:09

22.8k

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Prove that $\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$

Published on 13 Apr 2014 - 20:10

score 110 · Answer 2 · 2014-04-13 20:59:20

110

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Prove that $\sum\limits_{k=0}^n\ 2\times3^{k-1} = 3^n-1$

Published on 13 Apr 2014 - 20:59

score 79 · Answer 3 · 2014-04-13 22:57:36

79

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Proof by induction valid or not?

Published on 13 Apr 2014 - 22:57

score 64 · Answer 4 · 2026-03-25 11:06:56

64

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How to prove $\sum\limits_{k=0}^n\ (3k^2+2k+1) = n^3 + 5 \begin{pmatrix}n+1\\2\end{pmatrix}+1$

Published on 25 Mar 2026 - 11:06

score 130 · Answer 5 · 2014-04-14 02:54:46

130

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Why is this contrapostive assumed to be true?

Published on 14 Apr 2014 - 2:54

score 43 · Answer 6 · 2014-04-14 18:46:34

43

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Induction when not dealing with Sigma notation

Published on 14 Apr 2014 - 18:46

score 82 · Answer 7 · 2026-03-30 15:42:41

82

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so Thinking about induction proofs

Published on 30 Mar 2026 - 15:42

score 392 · Answer 8 · 2014-04-15 19:26:48

392

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Strong induction inequality $\frac{1}{2^3}+\frac{1}{3^3}+\cdots+\frac{1}{n^3}\leq\frac{5}{8}-\frac{1}{n}$

Published on 15 Apr 2014 - 19:26

score 52 · Answer 9 · 2026-03-26 18:58:17

52

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Could someone explain me this induction.

Published on 26 Mar 2026 - 18:58

score 317 · Answer 10 · 2014-04-15 22:16:46

317

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Induction: Sum of the squares of 6 consecutive natural numbers

Published on 15 Apr 2014 - 22:16

score 60 · Answer 11 · 2014-04-16 09:18:36

60

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Mathematical Induction for divisibility by $7$

Published on 16 Apr 2014 - 9:18

score 74 · Answer 12 · 2014-04-16 19:57:23

74

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Induction, show that something is smaller then ...

Published on 16 Apr 2014 - 19:57

score 1.8k · Answer 13 · 2026-04-02 16:51:24

1.8k

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Proof by induction of a recursive sequence

Published on 02 Apr 2026 - 16:51

score 64 · Answer 14 · 2026-03-28 06:48:32

64

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How have they done the algebra here?

Published on 28 Mar 2026 - 6:48

score 103 · Answer 15 · 2014-04-18 09:14:31

103

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Proving that $(a+b+c)^n=a^n + b^n + c^n$

Published on 18 Apr 2014 - 9:14

List Question

Prove that $\sum_{k=0}^n k^2{n \choose k} = {(n+n^2)2^{n-2}}$

Prove that $\sum\limits_{k=0}^n\ 2\times3^{k-1} = 3^n-1$

Proof by induction valid or not?

How to prove $\sum\limits_{k=0}^n\ (3k^2+2k+1) = n^3 + 5 \begin{pmatrix}n+1\\2\end{pmatrix}+1$

Why is this contrapostive assumed to be true?

Induction when not dealing with Sigma notation

so Thinking about induction proofs

Strong induction inequality $\frac{1}{2^3}+\frac{1}{3^3}+\cdots+\frac{1}{n^3}\leq\frac{5}{8}-\frac{1}{n}$

Could someone explain me this induction.

Induction: Sum of the squares of 6 consecutive natural numbers

Mathematical Induction for divisibility by $7$

Induction, show that something is smaller then ...

Proof by induction of a recursive sequence

How have they done the algebra here?

Proving that $(a+b+c)^n=a^n + b^n + c^n$

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