Question

If ${(1+ax)}^{11}=1+8x+24x^2+.....;$ then $\frac{a-n}{a+n}$ is equal to

Answer 1

⇒(a+x)n=1+8x+24x2+....By using Binomial

(a+x)n=an+C1nan−1x+C2nan−2x2+....

So

na=8n2a2=64And n(n−1)2a2=24

So

⇒n(n−1)2(64n2)=24

⇒2nn−1=83⇒6n=8n−8⇒n=4

So na=8

Hence a=2

Answer a=2 and n=4