Question

Find the coefficient of (r+1)th term in the expansion of (1+x)^n.​

Answer 1

Answer:

We know coefficient of (r+1)

th

term or x

r

in (1+x)

n+1

is =

n+1

C

r

Similarly coefficient of r

th

term or x

r−1

in (1+x)

n

is

n

C

r−1

and of (r+1)

th

term or x

r

in (1+x)

n

is

n

C

r

Consider

n

C

r

+

n

C

r−1

=

r!(n−r)!

n!

+

(r−1)!(n−r+1)!

n!

=

(r−1)!(n−r)!

n!

[

r

1

+

n−r+1

1

]

=

(r−1)!(n−r)!

n!

×

r(n−r+1)

(n+1)

=

n+1

C

r

Hence proved

Step-by-step explanation:

hope it helps you...