Question

$\pm 1$ combination of binomial coefficients that gives $0$

score 47 · Answer 1 · 2021-02-07 00:28:47

47

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$\pm 1$ combination of binomial coefficients that gives $0$

Published on 07 Feb 2021 - 0:28

score 1k · Answer 2 · 2026-03-26 17:53:41

1k

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Let $(2x^2 +3x+4)^{10} = \sum _{r=0}^{20} a_rx^r$. Then find $\frac{a_7}{a_{13}}$

Published on 26 Mar 2026 - 17:53

score 110 · Answer 3 · 2021-02-09 14:38:27

By choosing a suitable binomial expansion of the form $(1±kx)^n$ and a suitable value of x. Find $(1.01)^{20}$ correct to 3 s.f.

score 47 · Answer 4 · 2021-02-14 19:50:46

47

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How is this binomial coefficient be written in this way?

Published on 14 Feb 2021 - 19:50

score 45 · Answer 5 · 2026-02-24 01:32:07

45

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How was this simplification done?

Published on 24 Feb 2026 - 1:32

score 77 · Answer 6 · 2021-02-15 08:41:18

77

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Radius of convergence for series of $\frac{1}{x^2+\cos^2x}$

Published on 15 Feb 2021 - 8:41

score 45 · Answer 7 · 2021-02-19 19:44:12

45

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Show that $f(n, k) = \binom{n}{k}$ is an onto function

Published on 19 Feb 2021 - 19:44

score 178 · Answer 8 · 2026-03-27 11:48:19

178

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Question: For what value of $c$ will $P(x)= -2x^3+cx^2-5x+2$ have the same remainder when devided by $x+1$ or $x-2$?

Published on 27 Mar 2026 - 11:48

score 77 · Answer 9 · 2021-02-21 22:09:41

77

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What is the coefficient of $x^{11}$ in $(x+x^2+x^3+x^4+x^5)^4(1+x+x^2+...)^4$?

Published on 21 Feb 2021 - 22:09

score 613 · Answer 10 · 2021-02-22 06:39:59

613

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P is a set containing n elements. A subset 'A' of P is selected at random.

Published on 22 Feb 2021 - 6:39

score 82 · Answer 11 · 2021-02-25 14:20:11

82

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Given that $\frac{a}{1-x}+\frac{b}{1+2x}\approx-3+12x$ for small values of $x$, find the value of $a$ and $b$

Published on 25 Feb 2021 - 14:20

score 44 · Answer 12 · 2021-02-26 08:14:51

44

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Prove $(1+2/x)^{ -1}= x/x+2 = x/2(1+x/2)^{ -1}$

Published on 26 Feb 2021 - 8:14

score 47 · Answer 13 · 2026-02-24 01:39:06

47

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How to taylor expand $1/(1- \frac{k}{r})$ where k is some constant

Published on 24 Feb 2026 - 1:39

score 40 · Answer 14 · 2021-02-27 09:47:36

40

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Let $u_n=\sum_{r=0}^n (-1)^r \frac{\binom nr}{x+r}$ at $x=2$. Then find the sum to infinity of $u_1+u_2..$

Published on 27 Feb 2021 - 9:47

score 51 · Answer 15 · 2021-03-01 13:13:06

51

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Find the coefficient of $x^{9\ }$ in$\left(1+x\right)\left(1+x^{2}\right)\left(1+x^{3}\right)...\left(1+x^{100}\right)$

Published on 01 Mar 2021 - 13:13

List Question

$\pm 1$ combination of binomial coefficients that gives $0$

Let $(2x^2 +3x+4)^{10} = \sum _{r=0}^{20} a_rx^r$. Then find $\frac{a_7}{a_{13}}$

By choosing a suitable binomial expansion of the form $(1±kx)^n$ and a suitable value of x. Find $(1.01)^{20}$ correct to 3 s.f.

How is this binomial coefficient be written in this way?

How was this simplification done?

Radius of convergence for series of $\frac{1}{x^2+\cos^2x}$

Show that $f(n, k) = \binom{n}{k}$ is an onto function

Question: For what value of $c$ will $P(x)= -2x^3+cx^2-5x+2$ have the same remainder when devided by $x+1$ or $x-2$?

What is the coefficient of $x^{11}$ in $(x+x^2+x^3+x^4+x^5)^4(1+x+x^2+...)^4$?

P is a set containing n elements. A subset 'A' of P is selected at random.

Given that $\frac{a}{1-x}+\frac{b}{1+2x}\approx-3+12x$ for small values of $x$, find the value of $a$ and $b$

Prove $(1+2/x)^{ -1}= x/x+2 = x/2(1+x/2)^{ -1}$

How to taylor expand $1/(1- \frac{k}{r})$ where k is some constant

Let $u_n=\sum_{r=0}^n (-1)^r \frac{\binom nr}{x+r}$ at $x=2$. Then find the sum to infinity of $u_1+u_2..$

Find the coefficient of $x^{9\ }$ in$\left(1+x\right)\left(1+x^{2}\right)\left(1+x^{3}\right)...\left(1+x^{100}\right)$

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