In the expansion of ${(1 + x)^5}$, the sum of the coefficient of the terms is
$80$
$16$
$32$
$64$
(c) Sum of the coefficients = ${(1 + 1)^5}$= $2^5$ $= 32.$
The sum to $(n + 1)$ terms of the series $\frac{{{C_0}}}{2} – \frac{{{C_1}}}{3} + \frac{{{C_2}}}{4} – \frac{{{C_3}}}{5} + …$ is
In the polynomial $(x – 1)(x – 2)(x – 3)………….(x – 100),$ the coefficient of ${x^{99}}$ is
The coefficient of $x^{256}$ in the expansion of $(1-x)^{101}\left(x^{2}+x+1\right)^{100}$ is:
Coefficient of $x^{64}$ in the expansion of $(x – 1)^2(x – 2)^3(x – 3)^4(x – 4)^5 …. (x – 10)^{11}$
If ${\left( {1 + x} \right)^n} = {c_0} + {c_1}x + {c_2}{x^2} + {c_3}{x^3} + …… + {c_n}{x^n}$ , then the value of ${c_0} – 3{c_1} + 5{c_2} – …….. + {( – 1)^n}\,(2n + 1){c_n}$ is
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