Question

How to find the indicated term ?

`(x + 1/(2x^2))^12`, middle term

Answer 1

`231/16 x^-6`

Explanation:

Considering

#(a+b)^12=a^12 + 12 a^11 b + 66 a^10 b^2 + 220 a^9 b^3 + 495 a^8 b^4 + 792 a^7 b^5 + 924 a^6 b^6 + 792 a^5 b^7 + 495 a^4 b^8 + 220 a^3 b^9 + 66 a^2 b^10 + 12 a b^11 + b^12#

the middle term is `924 a^6 b^6` Here `a = x` and `b = 1/(2x^2)`

then `924 a^6 b^6 = 924 x^6/(2x^2)^6 = 924/2^6 x^-6 = 231/16 x^-6`