Single Choice

Sum of the coefficients of $$ (1 - x)^{25} $$ is

A$$-1$$
B$$1$$
C$$0$$
Correct Answer
D$$ 2^{25} $$

Solution

$$(1-x)\:^{25}$$ $$=1-\:^{25}C_{1}x+\:^{25}C_{2}x^2-\:^{25}C_{3}x^3+\:^{25}C_{4}x^4-\:^{25}C_{5}x^5...-\:^{25}C_{25}x^{25}$$
Putting $$x=1$$, we get
$$0=1-\:^{25}C_{1}+\:^{25}C_{2}-\:^{25}C_{3}+\:^{25}C_{4}-\:^{25}C_{5}...-\:^{25}C_{25}$$
Hence, sum of coefficients is $$0$$

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