In the expansion of ${(1 + x)^n}$ the sum of coefficients of odd powers of $x$ is
In the expansion of ${(1 + x)^n}$ the sum of coefficients of odd powers of $x$ is
- A
${2^n} + 1$
- B
${2^n} - 1$
- C
${2^n}$
- D
${2^{n - 1}}$
Similar Questions
The sum of the series $aC_0 + (a + b)C_1 + (a + 2b)C_2 + ..... + (a + nb)C_n$ is where $Cr's$ denotes combinatorial coefficient in the expansion of $(1 + x)^n, n \in N$
The sum of the series $aC_0 + (a + b)C_1 + (a + 2b)C_2 + ..... + (a + nb)C_n$ is where $Cr's$ denotes combinatorial coefficient in the expansion of $(1 + x)^n, n \in N$
${C_0}{C_r} + {C_1}{C_{r + 1}} + {C_2}{C_{r + 2}} + .... + {C_{n - r}}{C_n}$=
${C_0}{C_r} + {C_1}{C_{r + 1}} + {C_2}{C_{r + 2}} + .... + {C_{n - r}}{C_n}$=
In the polynomial $(x - 1)(x - 2)(x - 3).............(x - 100),$ the coefficient of ${x^{99}}$ is
In the polynomial $(x - 1)(x - 2)(x - 3).............(x - 100),$ the coefficient of ${x^{99}}$ is
If $\frac{{ }^{11} C_1}{2}+\frac{{ }^{11} C_2}{3}+\ldots . .+\frac{{ }^{11} C_9}{10}=\frac{n}{m}$ with $\operatorname{gcd}(n, m)=1$, then $n+m$ is equal to
If $\frac{{ }^{11} C_1}{2}+\frac{{ }^{11} C_2}{3}+\ldots . .+\frac{{ }^{11} C_9}{10}=\frac{n}{m}$ with $\operatorname{gcd}(n, m)=1$, then $n+m$ is equal to
- [JEE MAIN 2024]
The value of $^{15}C_0^2{ - ^{15}}C_1^2{ + ^{15}}C_2^2 - ....{ - ^{15}}C_{15}^2$ is
The value of $^{15}C_0^2{ - ^{15}}C_1^2{ + ^{15}}C_2^2 - ....{ - ^{15}}C_{15}^2$ is