If n is an integer greater than 1 , then a{ - ^n}{C₁}(a - 1){ + ^n}{C₂}(a - 2) + .... + {( - 1)^

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7.Binomial Theorem

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If $n$ is an integer greater than $1$, then $a{ - ^n}{C_1}(a - 1){ + ^n}{C_2}(a - 2) + .... + {( - 1)^n}(a - n) = $

A

$a$

B

$0$

C

${a^2}$

D

${2^n}$

(IIT-1972)

Solution

(b) $L.H.S. = a[{C_0} – {C_1} + {C_2} – {C_3} + …{( – 1)^n}.{C_n}]$$ + [{C_1} – 2{C_2} + 3{C_3} – …. + {( – 1)^{n – 1}}n.{C_n}]$

$ = a.0 + 0 = 0$

Standard 11

Mathematics

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