Question

find the first three terms in the expansion in ascending powers of x,of (2-x)
$(2 - x) {5}$
​

Answer 1

Answer:

Coefficient of x

r

and x

r+1

are equal.

Coefficient of T

r+1

= Coefficient of T

r+2

⇒

55

C

r

(2)

55−r

(

3

1

)

r

=

55

C

r+1

(2)

54−r

(

3

1

)

r+1

.

(55−r)!r!

55!

(2)=

(54−r)!(r+1)!

55!

3

1

⇒6(r+1)=55−r

⇒r=7

So, the terms will be 8

th

and 9

th

Step-by-step explanation:

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Answer 2

Answer:

Coefficient of x

r

and x

r+1

are equal.

Coefficient of T

r+1

= Coefficient of T

r+2

⇒

55

C

r

(2)

55−r

(

3

1

)

r

=

55

C

r+1

(2)

54−r

(

3

1

)

r+1

.

(55−r)!r!

55!

(2)=

(54−r)!(r+1)!

55!

3

1

⇒6(r+1)=55−r

⇒r=7

So, the terms will be 8

th

and 9

th

Step-by-step explanation:

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