List questions from binomial-theorem

Published on 10 Jul 2016 - 4:56

133

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$ z^n = a_n + b_ni $ Show that $ b_{n+2} - 2b_{n+1} + 5b_n = 0 $ (complex numbers)

Published on 12 Jul 2016 - 11:42

252

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$ z = 1 + 2i $ - Prove that $ z^n \notin \mathbb{R} $

Published on 12 Jul 2016 - 16:09

58

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If $f(n) =\displaystyle\sum_{r=1}^{n}\Biggl(r^n\Bigg(\binom{n}{r}-\binom{n}{r-1}\Bigg) + (2r+1)\binom{n}{r}\Biggr)$, then what is $f(30)$?

Published on 13 Jul 2016 - 16:01

26.1k

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Is there a formula for the binomial expansion of $(a-b)^n$?

Published on 16 Jul 2016 - 11:08

128

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Binomial Expansion: precalculus

Published on 16 Jul 2016 - 13:05

1.2k

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Identical Obects in Permutation and combination

Published on 21 Jul 2016 - 18:26

49

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Probability question, can I reset the window or not

Published on 22 Jul 2016 - 6:00

109

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Need help with inductive proof of Binomial Theorem

Published on 22 Jul 2016 - 23:58

1.9k

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Formation of Teams in Permutation and Combination

Published on 23 Jul 2016 - 8:09

75

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Find the coefficient of $x^n$ simply by using binomial theorem

Published on 23 Jul 2016 - 18:29

48

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Prove that: ${^{n}\mathrm{C}_{k}} = {^{n-1}\mathrm{C}_{k-1}}+{^{n-1}\mathrm{C}_{k}}$

Published on 30 Mar 2026 - 18:05

309

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Problem related to series of binomial coefficients

Published on 24 Jul 2016 - 10:08

162

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Find the value of $\sum_{r=0}^{\left\lfloor\frac{n-1}3\right\rfloor}\binom{n}{3r+1}$

Published on 24 Jul 2016 - 15:46

1k

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How do I find the terms of an expansion using combinatorial reasoning?

Published on 24 Jul 2016 - 23:05

List Question

Compute $\sum\limits_{k=0}^{100}\frac{1}{(100-k)!(100+k)!}$

$ z^n = a_n + b_ni $ Show that $ b_{n+2} - 2b_{n+1} + 5b_n = 0 $ (complex numbers)

$ z = 1 + 2i $ - Prove that $ z^n \notin \mathbb{R} $

If $f(n) =\displaystyle\sum_{r=1}^{n}\Biggl(r^n\Bigg(\binom{n}{r}-\binom{n}{r-1}\Bigg) + (2r+1)\binom{n}{r}\Biggr)$, then what is $f(30)$?

Is there a formula for the binomial expansion of $(a-b)^n$?

Binomial Expansion: precalculus

Identical Obects in Permutation and combination

Probability question, can I reset the window or not

Need help with inductive proof of Binomial Theorem

Formation of Teams in Permutation and Combination

Find the coefficient of $x^n$ simply by using binomial theorem

Prove that: ${^{n}\mathrm{C}_{k}} = {^{n-1}\mathrm{C}_{k-1}}+{^{n-1}\mathrm{C}_{k}}$

Problem related to series of binomial coefficients

Find the value of $\sum_{r=0}^{\left\lfloor\frac{n-1}3\right\rfloor}\binom{n}{3r+1}$

How do I find the terms of an expansion using combinatorial reasoning?

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