Question

Find the middle team in the expansion
of (X+1/X)⁴​

Answer 1

Answer:

(X+1/X)⁴

(x⁴+1lX⁴)

X⁴

Answer 2

Answer:

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Explanation:

Middle term =

2

N

+1

=

2

2n

+1

=(n+1)thterm

Now consider the following

T

r+1

=

n

C

r

a

n−r

b

r

...(i)

Where T represents the term

Here the middle term is the (n+1)

th

term.

Hence, r+1=n+1

r=n

Substituting in (i), we get

2n

C

n

1

2n−n

x

n

=

2n

C

n

x

n

Therefore the coefficient of the middle term is

2n

C

n

Substituting n=20, we get

40

C

20

=

20!20!

40!

Dividing by 20! and separating the multiples of two in the powers of two we get,

Middle term =

20!

(1.3.5.7....39)2

20