Question

The ratio of the coefficient of third and fourth term of an expansion is x minus 1 upon 2 x to the power n is 1 is to 2 then the value of n will be

Answer 1

Answer:

-10

Step-by-step explanation:

In binomial expansion (x+y)n,

General term =Tr+1=nCr.xn−r.yr

Now, in (x−12x)n

T3=nC2(x)n−2(−12x)2

⇒T3=nC2(x)n−2(122x2)

⇒T3=nC2(x)n−2−2(122)

⇒T3=nC2(x)n−4(14)---(1)

T4=nC3(x)n−3(−12x)3

⇒T3=nC3(x)n−2(−123x3)

⇒T3=−nC3(x)n−2−3(18)

⇒T3=−nC3(x)n−5(18)---(2)

It is given that, the ratio of the coefficient of third and fourth term is 1:2

⇒nC2.14−nC3.18=12

⇒nC2.14nC3.18=−12

⇒n(n−1)2.1n(n−1)(n−2)3.2.1.2=−12

⇒n(n−1)2.1×3.2.1n(n−1)(n−2).2=−12

⇒6n−2=−12

⇒12=−n+2

⇒n=2−12

⇒n=−10