if the 21st and 22nd terms in the expansion of (1+x)^44 are equal then find the value of x - Maths - Binomial Theorem

Question

if the 21st and 22nd terms in the expansion of (1+x)^44 are
equal then find the value of x

Shipra D. · Accepted Answer

The nth term of the binomial expansion 1+x44 is given as:

Tn=Cn-144x44-n-11n-1⇒T21=C2044x44-21-1121-1=C2044x24

And ⇒T22=C2144x44-22-1122-1=C2144x23

Now,

T21=T22⇒C2044x24=C2144x23⇒x=C2144C2044=44!21!23!44!20!24!=78

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