Question

find five term of the expansion
(x+y/2)^1/3

show step plz

Answer 1

(x+y/2)^1/3
= x^(1/3) + (1/3)(x^(-2/3) (y/2) + (1/3)(-2/3)/2! (x^(-5/3) )(y/2)^2 + (1/3)(-2/3)(-5/3)/3! (x^(-5/3))(y/2)^3 + ....
= x^(1/3) + (1/6)(x^(-2/3)y - (1/36)(x^(-5/3)y^2 + (5/648)x^(-8/3)y^3 + ???

I left out the 5th term for you to finish.
I am sure you can see the pattern

Answer 2

1/0! x^(1/3) (y/2)^0
+ (1/3)/1! x^(-2/3) (y/2)^1
+ (1/3)(-2/3)/2! x^(-5/3)(y/2)^2
+ (1/3)(-2/3)(-5/3)/3! x^(-8/3)(y/2)^3
+ (1/3)(-2/3)(-5/3)(-8/3)/4! x^(-11/3)(y/2)^4

= x^{^1/3}
+ 1/6 x^{^-2/3} y
- 1/36 x^{^-5/3} y^²
+ 5/648 x^{^-8/3} y^³
- 5/1944 x^{^-11/3} y^⁴