If $n \in N,\ n 1$, then value of $E = a - \ ^{n}C_{1}(a - 1) + \ ^{n}C_{2}(a - 2) + ... + ( - 1)^{n}(a - n)\ ^{n}C_{n}$ is

Question

If $n \in N,\ n > 1$, then value of $E = a - \ ^{n}C_{1}(a - 1) + \ ^{n}C_{2}(a - 2) + ... + ( - 1)^{n}(a - n)\ ^{n}C_{n}$ is

Dr. Abubacker · Accepted Answer

(b)
Given equation can be rewritten as
$E = a\left\lbrack \ ^{n}C_{0} - \ ^{n}C_{1} + \ ^{n}C_{2} - ... + {( - 1)}^{n}\ ^{n}C_{n} \right\rbrack + \left\lbrack \ ^{n}C_{1} - (2)\left( \ ^{n}C_{2} \right) + (3)\left( \ ^{n}C_{3} \right) - ... + ( - 1)^{n}(n){\ (}^{n}C_{n}) \right\rbrack$
$\Rightarrow E = 0 + 0 = 0$ (by properties)

Q. If $n \in N,\ n > 1$, then value of $E = a - \ ^{n}C_{1}(a - 1) + \ ^{n}C_{2}(a - 2) + ... + ( - 1)^{n}(a - n)\ ^{n}C_{n}$ is

Explanation

Reviewed by Dr. Abubacker

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