Question

Prove that the coefficient of



in the expansion of (1 + )

2

is twice the coefficient of



in the

expansion of (1 + )

2−1

.​

Answer 1

Step-by-step explanation:

We know that

General term of (a+b)

n

is

T

r+1

=

n

C

r

a

n−r

,b

r

For (1+x)

2n

General term of (1+x)

2n

Putting a=1,b=x,n=2n

T

r+1

=

2n

C

r

1

2n−r

(x)

r

T

r+1

=

2n

C

r

x

r

…………….(1)

For coefficient of x

n

Putting r=n in (1)

T

r+1

=

2n

C

n

x

n

Coefficient of x

n

=

2n

C

n

For (1+x)

Answer 2

Answer:

Pilavullakandi Thekkeparambil Usha is a retired Indian track and field athlete. She has been associated with Indian athletics since 1979. She is often called the "queen of Indian track and field".

Born: 27 June 1964 (age 56 years), Payyoli

Spouse: V Srinivasan (m. 1991)

Nickname(s): Golden Girl, Payyoli Express

Event(s): Sprints

Awards: Arjuna Award for Athletics, Padma Shri

Books: Golden Girl: The Autobiography of P.T. Usha

Children: Vignesh Ujjwal, Ujjwal Srinivasan