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Question: If (1 + ax)<sup>n</sup> = 1 + 8x + 24x<sup>2</sup> +……; then \(\frac{a - n}{a + n}\) is equal to –...

If (1 + ax)n = 1 + 8x + 24x2 +……; then a−na+n\frac{a - n}{a + n} is equal to –

A

3

B

–3

C

–1/3

D

1/3

Answer

–1/3

Explanation

Solution

nC0 + nC1 (ax) + nC2 (ax)2 + nC3 (ax)3 + ......

= 1 + 8x + 24 x2 + .....

Ž an = 8 & n(n−1)2\frac{n(n - 1)}{2}a2 = 24

(n−1)2n\frac{(n - 1)}{2n}= 248(8)\frac{24}{8(8)} Ž 4n – 4 = 3n

Ž n = 4 Ž a = 2

a−na+n\frac{a - n}{a + n}= –13\frac{1}{3}