Question

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

score 4.2k · Answer 1 · 2020-12-25 15:42:07

4.2k

Views

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

Published on 25 Dec 2020 - 15:42

score 1.8k · Answer 2 · 2020-12-27 07:55:32

1.8k

Views

Question on binomial theorem: Find the term independent of $x$ in the expansion of $(2+x)\left(2x+\frac{1}{x}\right)^5$

Published on 27 Dec 2020 - 7:55

score 67 · Answer 3 · 2021-01-02 04:08:47

67

Views

proving $\displaystyle\sum_{s,r=0,s\ne r}^{n}C_rC_s=\frac{1}{2}\left(2^{2n}-\frac{(2n)!}{(n!)^2}\right)$

Published on 02 Jan 2021 - 4:08

score 89 · Answer 4 · 2026-03-25 19:02:45

89

Views

Prove that $e^{\frac{x+y}{2}} \le \frac{e^x + e^y}{2}$

Published on 25 Mar 2026 - 19:02

score 64 · Answer 5 · 2021-01-03 14:20:55

64

Views

Find $[(\sqrt 2 +1)^8]$, where $[.]$ is integer part function

Published on 03 Jan 2021 - 14:20

score 56 · Answer 6 · 2021-01-03 14:24:51

56

Views

$R=(3+\sqrt 5)^{2n}$ and $f=R-[R]$, where $[.]$ is an integer part function. Then find $R(1-f)$

Published on 03 Jan 2021 - 14:24

score 62 · Answer 7 · 2021-01-03 16:23:20

62

Views

If $(1+x+x^2)^n = C_0 + C_1x + C_2 x^2...$, then find $C_0C_1 -C_1C_2 + C_2C_3...$

Published on 03 Jan 2021 - 16:23

score 40 · Answer 8 · 2021-01-05 19:56:43

40

Views

binomial-coefficients question $(\frac{x\sqrt[3]{x}}{2}+\frac{1}{\sqrt[15]{x^28}})^n$

Published on 05 Jan 2021 - 19:56

score 66 · Answer 9 · 2026-03-26 14:30:25

66

Views

How many rational elements are in the multinomial? $(\sqrt[3]{x}+\sqrt[5]{x}+2\sqrt{x})^5$

Published on 26 Mar 2026 - 14:30

score 258 · Answer 10 · 2026-02-24 01:31:19

258

Views

Negative Binomial Series

Published on 24 Feb 2026 - 1:31

score 86 · Answer 11 · 2021-01-09 11:59:23

86

Views

Number of way choose ordered distinct quadruples $(A,B,C,D)$ from $\{1,2,...,n\}(n\geq 2)$

Published on 09 Jan 2021 - 11:59

score 178 · Answer 12 · 2021-01-09 17:38:10

178

Views

How can you prove n= $6k +2$ when the $x^2$ and $x^3$ coefficient of $(2k +x)^n$ is the same?

Published on 09 Jan 2021 - 17:38

score 70 · Answer 13 · 2021-01-12 14:49:53

70

Views

Regarding the values that n and r can take in $\binom{n}{r}$

Published on 12 Jan 2021 - 14:49

score 79 · Answer 14 · 2021-01-12 20:08:45

79

Views

I came across this problem in Binomial Theorem. I need help in proving this.

Published on 12 Jan 2021 - 20:08

score 47 · Answer 15 · 2021-01-15 04:45:00

47

Views

Finding the sum of a geometric binomial progression

Published on 15 Jan 2021 - 4:45

List Question

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

Question on binomial theorem: Find the term independent of $x$ in the expansion of $(2+x)\left(2x+\frac{1}{x}\right)^5$

proving $\displaystyle\sum_{s,r=0,s\ne r}^{n}C_rC_s=\frac{1}{2}\left(2^{2n}-\frac{(2n)!}{(n!)^2}\right)$

Prove that $e^{\frac{x+y}{2}} \le \frac{e^x + e^y}{2}$

Find $[(\sqrt 2 +1)^8]$, where $[.]$ is integer part function

$R=(3+\sqrt 5)^{2n}$ and $f=R-[R]$, where $[.]$ is an integer part function. Then find $R(1-f)$

If $(1+x+x^2)^n = C_0 + C_1x + C_2 x^2...$, then find $C_0C_1 -C_1C_2 + C_2C_3...$

binomial-coefficients question $(\frac{x\sqrt[3]{x}}{2}+\frac{1}{\sqrt[15]{x^28}})^n$

How many rational elements are in the multinomial? $(\sqrt[3]{x}+\sqrt[5]{x}+2\sqrt{x})^5$

Negative Binomial Series

Number of way choose ordered distinct quadruples $(A,B,C,D)$ from $\{1,2,...,n\}(n\geq 2)$

How can you prove n= $6k +2$ when the $x^2$ and $x^3$ coefficient of $(2k +x)^n$ is the same?

Regarding the values that n and r can take in $\binom{n}{r}$

I came across this problem in Binomial Theorem. I need help in proving this.

Finding the sum of a geometric binomial progression

Trending Questions

Popular # Hahtags

Popular Questions