Question

2. Show that the ratio of the coefficient of x10 in (1 - x-)10 and the term independent
10
ofx in (x – 3)' is (1:32).
A​

Answer 1

Answer:

To Prove : coefficient of x10 in (1-x2)10: coefficient of x0 in

= 1:32

For (1-x2)10 ,

Here, a=1, b=-x2 and n=15

We have formula,

To get coefficient of x10 we must have,

(x)2r = x10

• 2r = 10

• r = 5

Therefore, coefficient of x10

For

,

Here, a=x,

and n=10

We have a formula,

Now, to get coefficient of term independent of xthat is coefficient of x0 we must have,

(x)10-2r = x0

• 10 - 2r = 0

• 2r = 10

• r = 5

Therefore, coefficient of x0

Therefore,

Hence,

coefficient of x10 in (1-x2)10: coefficient of x0 in

= 1:32