Question

Prove $\sum_{k=0}^{m}\binom{n}{k}(n-2k)(-1)^k=0$

score 248 · Answer 1 · 2026-03-27 18:02:50

248

Views

Prove $\sum_{k=0}^{m}\binom{n}{k}(n-2k)(-1)^k=0$

Published on 27 Mar 2026 - 18:02

score 42 · Answer 2 · 2026-03-25 23:15:58

42

Views

Upper bound on some sum

Published on 25 Mar 2026 - 23:15

score 282 · Answer 3 · 2018-07-19 23:20:43

282

Views

Can this kind of curve ever be convergent?

Published on 19 Jul 2018 - 23:20

score 65 · Answer 4 · 2026-03-26 23:11:44

65

Views

Having trouble with a Binomial proof by mathematical induction question: $\sum_{j=3}^n \binom{j-1}{2} = \binom{n}{3}$

Published on 26 Mar 2026 - 23:11

score 75 · Answer 5 · 2018-07-20 13:15:04

75

Views

Convert following phrase in terms of sigma notation format?

Published on 20 Jul 2018 - 13:15

score 119 · Answer 6 · 2026-03-26 14:22:13

119

Views

The number of combinations of Fi to F255 that satisfies the following inequality.

Published on 26 Mar 2026 - 14:22

score 67 · Answer 7 · 2018-07-21 16:37:32

67

Views

Writing a polynomial as product of its roots

Published on 21 Jul 2018 - 16:37

score 158 · Answer 8 · 2018-07-22 13:11:27

158

Views

Compute $\lim\limits_{x\to \infty }\sum\limits_{n=1}^\infty \frac{1}{n(n+x)}$

Published on 22 Jul 2018 - 13:11

score 95 · Answer 9 · 2026-03-27 18:02:53

95

Views

My induction does not prove my conjecture. Is my conjecture wrong or is my induction insufficient/wrong?

Published on 27 Mar 2026 - 18:02

score 536 · Answer 10 · 2018-07-22 15:11:15

536

Views

Partial sums of the series $\sum\limits_{k\geq1}\frac{1}{\sqrt{2k+\sqrt{4k^2-1}}}$

Published on 22 Jul 2018 - 15:11

score 1k · Answer 11 · 2018-07-22 17:18:33

1k

Views

Summation rules and properties

Published on 22 Jul 2018 - 17:18

score 31 · Answer 12 · 2018-07-22 18:15:23

31

Views

Solve $\frac{d}{da_k}\big[\sum_{k=1}^{p}{-a_k\cdot y(n-k)}\big]$

Published on 22 Jul 2018 - 18:15

score 35 · Answer 13 · 2026-03-28 10:24:12

35

Views

This transform gives the coefficients of the preimage of a polynomial isomorphism; what is its name?

Published on 28 Mar 2026 - 10:24

score 2.4k · Answer 14 · 2026-03-26 23:09:51

2.4k

Views

Prove $\binom{2n}{n}~=~\sum_{k=0}^n \binom{n}{k}^2$

Published on 26 Mar 2026 - 23:09

score 174 · Answer 15 · 2018-07-23 16:23:04

174

Views

Find the sum of $2^{-x}/x$

Published on 23 Jul 2018 - 16:23

List Question

Prove $\sum_{k=0}^{m}\binom{n}{k}(n-2k)(-1)^k=0$

Upper bound on some sum

Can this kind of curve ever be convergent?

Having trouble with a Binomial proof by mathematical induction question: $\sum_{j=3}^n \binom{j-1}{2} = \binom{n}{3}$

Convert following phrase in terms of sigma notation format?

The number of combinations of Fi to F255 that satisfies the following inequality.

Writing a polynomial as product of its roots

Compute $\lim\limits_{x\to \infty }\sum\limits_{n=1}^\infty \frac{1}{n(n+x)}$

My induction does not prove my conjecture. Is my conjecture wrong or is my induction insufficient/wrong?

Partial sums of the series $\sum\limits_{k\geq1}\frac{1}{\sqrt{2k+\sqrt{4k^2-1}}}$

Summation rules and properties

Solve $\frac{d}{da_k}\big[\sum_{k=1}^{p}{-a_k\cdot y(n-k)}\big]$

This transform gives the coefficients of the preimage of a polynomial isomorphism; what is its name?

Prove $\binom{2n}{n}~=~\sum_{k=0}^n \binom{n}{k}^2$

Find the sum of $2^{-x}/x$

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