List questions from binomial-theorem

Published on 26 Aug 2017 - 19:54

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Show that for any integer $n\ge 6$, the inequality $2^n>7n$ holds.

Published on 27 Aug 2017 - 14:56

4.2k

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In expansion of $(1+x+x^{2}+x^{3}+....+x^{27})(1+x+x^{2}+x^{3}+....x^{14})^{2}$ . Find the coefficient of $x^{28}$

Published on 28 Aug 2017 - 10:28

213

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Probability Finance Question

Published on 04 Apr 2026 - 0:10

136

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I need help in proving an identity about the Inclusion exclusion principle

Published on 03 Apr 2026 - 15:46

5k

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If the constant term of binomial expansion $ (2x-\frac{1}{x})^{n}$ is$-160$ ,then $n$ equal to?

Published on 29 Aug 2017 - 12:13

49

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Combinatorics: n people visit k exhibitions

Published on 29 Aug 2017 - 16:59

61

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Lower bound for binomial theorem for $\frac{n}{2}$

Published on 30 Aug 2017 - 23:43

4.1k

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Binomial Expansion conditions for valid expansion $\frac{1}{(1+4x)^2}$

Published on 02 Sep 2017 - 13:12

190

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Evaluate sum similar to the binomial theorem modulo 5

Published on 03 Sep 2017 - 9:15

262

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Is this sum $\sum_{k=0}^{n}{n\choose k}\sum_{i=0}^{k}(-1)^i{k\choose i}H_{n+k-i}=H_{2n}$ correct?

Published on 30 Mar 2026 - 7:09

65

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math induction help?

Published on 08 Sep 2017 - 4:34

569

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Condition for using binomial theorem for negative index

Published on 08 Sep 2017 - 17:38

117

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Non negative solutions and generating functions

Published on 09 Sep 2017 - 12:20

157

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Generating functions for the solutions to $3x_1 + x_2 = n$

Published on 09 Sep 2017 - 13:37

List Question

Summation of some factorial terms

Show that for any integer $n\ge 6$, the inequality $2^n>7n$ holds.

In expansion of $(1+x+x^{2}+x^{3}+....+x^{27})(1+x+x^{2}+x^{3}+....x^{14})^{2}$ . Find the coefficient of $x^{28}$

Probability Finance Question

I need help in proving an identity about the Inclusion exclusion principle

If the constant term of binomial expansion $ (2x-\frac{1}{x})^{n}$ is$-160$ ,then $n$ equal to?

Combinatorics: n people visit k exhibitions

Lower bound for binomial theorem for $\frac{n}{2}$

Binomial Expansion conditions for valid expansion $\frac{1}{(1+4x)^2}$

Evaluate sum similar to the binomial theorem modulo 5

Is this sum $\sum_{k=0}^{n}{n\choose k}\sum_{i=0}^{k}(-1)^i{k\choose i}H_{n+k-i}=H_{2n}$ correct?

math induction help?

Condition for using binomial theorem for negative index

Non negative solutions and generating functions

Generating functions for the solutions to $3x_1 + x_2 = n$

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