Question

if 21st and 22nd term in the expansion of (1+x)^44 are equal. find x​

Answer 1

The nth term of the binomial expansion (1+x)44 is given as:

Tn=Cn−144(x)44−(n−1)(1)n−1⇒T21=C2044(x)44−(21−1)(1)21−1=C2044(x)24

And ⇒T22=C2144(x)44−(22−1)(1)22−1=C2144(x)23

Now,

T21=T22⇒C2044(x)24=C2144(x)23⇒x=C2144C2044=(44!)(21!)(23!)(44!)(20!)(24!)=78