List questions from binomial-theorem

Published on 03 May 2026 - 12:39

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Finding coefficient in the expansion

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How to find the missing terms

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Solving the following equation with imaginary roots

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GATE $2018$ - Probability question : The probability that one of them wins on the third trial is ____ .

Published on 07 May 2026 - 10:12

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Deriving the power series for $e$ simply?

Published on 02 May 2026 - 18:19

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How do I find $\sum_{k=2}^nk(k-1)\binom{n}{k}$

Published on 11 Apr 2026 - 16:38

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Find, $\sum_{k=0}^{n}4^k \binom{n}{k}$

Published on 17 Apr 2026 - 13:55

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Proof of inequalities using binomial theorem

Published on 10 Apr 2026 - 2:50

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Prove that for positive integers $m, n$ and two positive numbers $p, q$ satisfying $p+q = 1$ we have $(1 − p^n)^m + (1 − q^m)^n \ge 1$.

Published on 17 Apr 2026 - 14:36

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If $x+y=1$ then $x^{n+1}\sum\limits_{k=0}^n \binom{n+k}{k}y^k+y^{n+1}\sum\limits_{k=0}^n \binom{n+k}{k}x^k=1$

Published on 16 Apr 2026 - 5:31

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For all $n\in\mathbb{N}$, let $a_n$ denote the number of strings of length $n$ over $\{1,2,3,4\}$ such that:

Published on 16 Apr 2026 - 5:45

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Finding greatest integer less than or equal to $(\sqrt{b}+a)^n$ if $|{\sqrt{b}-a}|>1$

Published on 16 Apr 2026 - 8:41

390

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Evaluate $\sum_{k=1}^n\frac{1}{k}\binom{n}{k}$

Published on 07 May 2026 - 13:20

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Deriving the derivative rule for monomials

Published on 10 Apr 2026 - 6:40

List Question

Sum of $\frac{C_r}{(r+1)(r+2)}$ from $r=0$ to $r=n$

Finding coefficient in the expansion

How to find the missing terms

Solving the following equation with imaginary roots

GATE $2018$ - Probability question : The probability that one of them wins on the third trial is ____ .

Deriving the power series for $e$ simply?

How do I find $\sum_{k=2}^nk(k-1)\binom{n}{k}$

Find, $\sum_{k=0}^{n}4^k \binom{n}{k}$

Proof of inequalities using binomial theorem

Prove that for positive integers $m, n$ and two positive numbers $p, q$ satisfying $p+q = 1$ we have $(1 − p^n)^m + (1 − q^m)^n \ge 1$.

If $x+y=1$ then $x^{n+1}\sum\limits_{k=0}^n \binom{n+k}{k}y^k+y^{n+1}\sum\limits_{k=0}^n \binom{n+k}{k}x^k=1$

For all $n\in\mathbb{N}$, let $a_n$ denote the number of strings of length $n$ over $\{1,2,3,4\}$ such that:

Finding greatest integer less than or equal to $(\sqrt{b}+a)^n$ if $|{\sqrt{b}-a}|>1$

Evaluate $\sum_{k=1}^n\frac{1}{k}\binom{n}{k}$

Deriving the derivative rule for monomials

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