Find the middle term in the expansion of #(x^2+1)^18#?

1 Answer
Mar 27, 2018

Middle term in the expansion of #(x^2+1)^18# is #48620x^18#

Explanation:

In the expansion of #(x+a)^n#, there are #(n+1)# terms and #r^(th)# term is #C_r^nx^(n-r)a^r#, where #r# ranges from #0# to #18#.

Hence there are #18+1=19# terms in the expansion of #(x^2+1)^18#

and middle term is #(19+1)/2=10# i.e. #10^(th)# term and as terms start from #r=0#, #10^(th)# term is for #r=9#

and it is #C_9^18(x^2)^(18-9)*1^9#

= #(18*17*16*15*14*13*12*11*10)/(1*2*3*4*5*6*7*8*9)*x^18*1#

= #48620x^18#