List questions from binomial-theorem

Published on 25 Oct 2016 - 18:28

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Divisibility of $8^{2000}+12^{2000}-5^{2000}-1$

Published on 26 Oct 2016 - 19:22

66

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Induction proof with binomials

Published on 27 Oct 2016 - 20:55

656

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Find the biggest term of an expansion

Published on 28 Oct 2016 - 17:30

51

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Binomial law problem

Published on 01 Nov 2016 - 2:50

88

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How to find the possible positive integer values of $k$ and $n$ in a binomial expansion.

Published on 01 Nov 2016 - 18:08

24.9k

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Binomial Theorem for Fractional Powers

Published on 03 Nov 2016 - 8:50

1.2k

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Coefficient of a term using binomial theorem

Published on 26 Mar 2026 - 1:34

35

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Show that for every even $n$, ${^nC}_0 - 2\cdot{^nC}_1 + 2^2\cdot{^nC}_2 -\dotsb+2^n\cdot{^nC}_n = 1$

Published on 05 Nov 2016 - 23:50

71

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Prove inequality by induction $\forall n \in \mathbb{N}, n\ge 2 \ \ : \ \ (1+\frac1n)^n<\sum\limits_{k=0}^n \frac1{k!}<3$

Published on 31 Mar 2026 - 3:39

36

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Show that $(1-\beta)(p+\beta)=1$

Published on 07 Nov 2016 - 2:51

1k

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Find the coefficient of $x^{16}$ in expansion of $(x^2+5x+6)^4(x^3+6x^2+11x+6)^3$.

Published on 07 Nov 2016 - 4:55

471

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Find the sum of series.

Published on 08 Nov 2016 - 7:22

235

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Prove inequality of binomial theorem $\frac1{n^i}\binom{n}i \leq\frac1{m^i}\binom{m}i $.

Published on 08 Nov 2016 - 10:12

37

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Finding the $(r+1)^{\text{th}}$ term of the binomial theorem

Published on 10 Nov 2016 - 1:37

List Question

Term independent of x and y in this expansion

Divisibility of $8^{2000}+12^{2000}-5^{2000}-1$

Induction proof with binomials

Find the biggest term of an expansion

Binomial law problem

How to find the possible positive integer values of $k$ and $n$ in a binomial expansion.

Binomial Theorem for Fractional Powers

Coefficient of a term using binomial theorem

Show that for every even $n$, ${^nC}_0 - 2\cdot{^nC}_1 + 2^2\cdot{^nC}_2 -\dotsb+2^n\cdot{^nC}_n = 1$

Prove inequality by induction $\forall n \in \mathbb{N}, n\ge 2 \ \ : \ \ (1+\frac1n)^n<\sum\limits_{k=0}^n \frac1{k!}<3$

Show that $(1-\beta)(p+\beta)=1$

Find the coefficient of $x^{16}$ in expansion of $(x^2+5x+6)^4(x^3+6x^2+11x+6)^3$.

Find the sum of series.

Prove inequality of binomial theorem $\frac1{n^i}\binom{n}i \leq\frac1{m^i}\binom{m}i $.

Finding the $(r+1)^{\text{th}}$ term of the binomial theorem

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