Question

How is $C_0^nC_n^{n+1}+ C_1^nC_{n-1}^{n}+C_2^nC_{n-2}^{n-1}+\dots+C_n^n C_0^{1} =2^{n-1}(n+2) ?$

score 131 · Answer 1 · 2018-11-03 07:09:31

131

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How is $C_0^nC_n^{n+1}+ C_1^nC_{n-1}^{n}+C_2^nC_{n-2}^{n-1}+\dots+C_n^n C_0^{1} =2^{n-1}(n+2) ?$

Published on 03 Nov 2018 - 7:09

score 123 · Answer 2 · 2018-11-03 09:43:18

123

Views

If $y=\frac25+\frac{1\cdot3}{2!}\left(\frac25\right)^2 +\frac{1\cdot3\cdot5}{3!}\left(\frac25\right)^3+\ldots$ then what is the value of $y^2+2y$?

Published on 03 Nov 2018 - 9:43

score 102 · Answer 3 · 2018-11-05 18:40:56

102

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How to find the sum of the given series: $\sum_{k=0}^{\min(n ,m)} \binom{n}{k} \binom{m}{k}$?

Published on 05 Nov 2018 - 18:40

score 164 · Answer 4 · 2018-11-07 05:57:42

164

Views

How can I find the number of dissimilar or distinct terms in $(1+x + x^2 +x^3)^n$?

Published on 07 Nov 2018 - 5:57

score 46 · Answer 5 · 2018-11-07 17:49:06

46

Views

Evaluate $lim_{n \to \infty} (n + 1)^{\frac{2}{3}} - (n)^{\frac{2}{3}}$ using the generalized binomial theorem

Published on 07 Nov 2018 - 17:49

score 45 · Answer 6 · 2018-11-08 04:46:00

45

Views

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Published on 08 Nov 2018 - 4:46

score 395 · Answer 7 · 2018-11-08 14:42:09

395

Views

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Published on 08 Nov 2018 - 14:42

score 98 · Answer 8 · 2018-11-11 23:40:32

98

Views

Showing that $\left(1+\frac{\varepsilon^2}{17n}\right)^n-1\leq \frac{\varepsilon^2}{16}$ when $0\leq \varepsilon\leq 1$

Published on 11 Nov 2018 - 23:40

score 202 · Answer 9 · 2018-11-13 15:28:21

202

Views

Binomial Expansion rth term

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score 296 · Answer 10 · 2018-11-14 16:29:38

296

Views

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score 238 · Answer 11 · 2018-11-14 17:09:07

238

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score 159 · Answer 12 · 2018-11-19 23:12:37

159

Views

How does it follow from the Pascal's Triangle that binomial coefficient are integers

Published on 19 Nov 2018 - 23:12

score 104 · Answer 13 · 2018-11-22 18:29:11

104

Views

I tried this question by using pi denoting method and got a big equation what to do

Published on 22 Nov 2018 - 18:29

score 170 · Answer 14 · 2026-03-25 16:14:01

170

Views

Proving $\int ^{2\pi} _{0} (\cos(t)^{2n})={2n \choose {n}}\frac{2\pi}{2^{2n}}$

Published on 25 Mar 2026 - 16:14

score 101 · Answer 15 · 2018-11-25 17:09:19

101

Views

How to show that $2^n > n$ without induction

Published on 25 Nov 2018 - 17:09

List Question

How is $C_0^nC_n^{n+1}+ C_1^nC_{n-1}^{n}+C_2^nC_{n-2}^{n-1}+\dots+C_n^n C_0^{1} =2^{n-1}(n+2) ?$

If $y=\frac25+\frac{1\cdot3}{2!}\left(\frac25\right)^2 +\frac{1\cdot3\cdot5}{3!}\left(\frac25\right)^3+\ldots$ then what is the value of $y^2+2y$?

How to find the sum of the given series: $\sum_{k=0}^{\min(n ,m)} \binom{n}{k} \binom{m}{k}$?

How can I find the number of dissimilar or distinct terms in $(1+x + x^2 +x^3)^n$?

Evaluate $lim_{n \to \infty} (n + 1)^{\frac{2}{3}} - (n)^{\frac{2}{3}}$ using the generalized binomial theorem

How to prove Binomial Theorem

Proof of Newton's Generalized Binomial Theorem (without Calculus)

Showing that $\left(1+\frac{\varepsilon^2}{17n}\right)^n-1\leq \frac{\varepsilon^2}{16}$ when $0\leq \varepsilon\leq 1$

Binomial Expansion rth term

Strengthening of Bernstein Inequality

Strict Bernstein Inequality

How does it follow from the Pascal's Triangle that binomial coefficient are integers

I tried this question by using pi denoting method and got a big equation what to do

Proving $\int ^{2\pi} _{0} (\cos(t)^{2n})={2n \choose {n}}\frac{2\pi}{2^{2n}}$

How to show that $2^n > n$ without induction

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