Question

A problem related to binomial theorem for any index

score 40 · Answer 1 · 2020-01-23 00:33:23

40

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A problem related to binomial theorem for any index

Published on 23 Jan 2020 - 0:33

score 30 · Answer 2 · 2020-01-25 15:12:23

30

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Solution verification: $f(x)=\frac{x^2}{(x^3-4)^{\frac13}}$ series expansion at positive and negative $\infty$

Published on 25 Jan 2020 - 15:12

score 131 · Answer 3 · 2020-01-26 06:23:46

131

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Binomial expansions of index

Published on 26 Jan 2020 - 6:23

score 51 · Answer 4 · 2020-01-29 01:57:23

51

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If $\sum_{0}^{2n}a_r(x-2)^r=\sum_{0}^{2n}b_r(x-3)^r$ and $a_k=1$ $\forall$ $k\ge n$, then show that $b_n=\displaystyle{2n+1\choose n+1}$

Published on 29 Jan 2020 - 1:57

score 205 · Answer 5 · 2020-01-29 02:40:58

205

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Prove that $\dfrac{72!}{(36!)^2}-1$ is divisible by $73$

Published on 29 Jan 2020 - 2:40

score 178 · Answer 6 · 2026-03-26 22:14:02

178

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Simplifying $\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - \binom{n}{3} + \cdots + (-1)^n \binom{n}{n}$

Published on 26 Mar 2026 - 22:14

score 31 · Answer 7 · 2020-02-01 17:38:26

31

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Finding the term in binomial theorem.

Published on 01 Feb 2020 - 17:38

score 137 · Answer 8 · 2020-02-01 22:53:54

137

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In how many ways can we place $k$ distinct objects into $n$ identical boxes if each box contains atmost one object

Published on 01 Feb 2020 - 22:53

score 69 · Answer 9 · 2020-02-05 19:29:46

69

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How to prove: If $n \in N$, then $n^2=2\binom{n}{2} + \binom{n}{1}$

Published on 05 Feb 2020 - 19:29

score 653 · Answer 10 · 2020-02-07 07:03:22

653

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Divisibility of $^{72}C_{36}$

Published on 07 Feb 2020 - 7:03

score 1.9k · Answer 11 · 2020-02-10 06:41:48

1.9k

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Finding the exponent $n$ in a binomial expansion given that the coefficient of $x^3$ is 4 times greater than the coefficient of $x^2$

Published on 10 Feb 2020 - 6:41

score 340 · Answer 12 · 2020-02-13 07:01:33

340

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prove $ \sum_{m=0}^{n-k} {n-m-1\choose n-k-m} \\ = [z^{n-k}] (1+z)^{n-1} \sum_{m=0}^{n-k} z^m (1+z)^{-m} $

Published on 13 Feb 2020 - 7:01

score 162 · Answer 13 · 2020-02-15 20:07:27

162

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Binomial theorem for exponential of nilpotent matrix

Published on 15 Feb 2020 - 20:07

score 1k · Answer 14 · 2020-02-16 13:52:32

1k

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Proof for Vandermonde's identity: ${{m+n} \choose r} = \sum_{k=0}^r {m \choose k}{n\choose {r-k}}$

Published on 16 Feb 2020 - 13:52

score 63 · Answer 15 · 2020-02-17 18:41:50

63

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Showing that a series has radius of convergence equal to 1

Published on 17 Feb 2020 - 18:41

List Question

A problem related to binomial theorem for any index

Solution verification: $f(x)=\frac{x^2}{(x^3-4)^{\frac13}}$ series expansion at positive and negative $\infty$

Binomial expansions of index

If $\sum_{0}^{2n}a_r(x-2)^r=\sum_{0}^{2n}b_r(x-3)^r$ and $a_k=1$ $\forall$ $k\ge n$, then show that $b_n=\displaystyle{2n+1\choose n+1}$

Prove that $\dfrac{72!}{(36!)^2}-1$ is divisible by $73$

Simplifying $\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - \binom{n}{3} + \cdots + (-1)^n \binom{n}{n}$

Finding the term in binomial theorem.

In how many ways can we place $k$ distinct objects into $n$ identical boxes if each box contains atmost one object

How to prove: If $n \in N$, then $n^2=2\binom{n}{2} + \binom{n}{1}$

Divisibility of $^{72}C_{36}$

Finding the exponent $n$ in a binomial expansion given that the coefficient of $x^3$ is 4 times greater than the coefficient of $x^2$

prove $ \sum_{m=0}^{n-k} {n-m-1\choose n-k-m} \\ = [z^{n-k}] (1+z)^{n-1} \sum_{m=0}^{n-k} z^m (1+z)^{-m} $

Binomial theorem for exponential of nilpotent matrix

Proof for Vandermonde's identity: ${{m+n} \choose r} = \sum_{k=0}^r {m \choose k}{n\choose {r-k}}$

Showing that a series has radius of convergence equal to 1

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