For the expression (1+x)24,n=24 (1+x)n=C0+C1x+C2x2+........+Crxr+.......+Cn−1xn−1+Cnxn Let's say that the successive terms at (r−1)th and rth place are the required terms. ∴
Cr
Cr−1
=
4
1
Let us simplify
Cr
Cr−1
Cr
Cr−1
=
n!
r!(n−r)!
n!
(r−1)![(n−(r−1)]!
=
(r−1)!(n−r+1)!
r!(n−r)!
=
n−r+1
r
∴
24−r+1
r
=
4
1
⇒24−r+1=4r ⇒5r=25 ⇒r=5 ∴ The required terms are at r−1=5−1=4th place and r=5th place.