Question

Find the middle term in the following expansion

( x+ 2/x) 8​

Answer 1

Answer:

12455

Step-by-step explanation:

567777377477474

Answer 2

Answer: 1120

Step-by-step explanation:

When we compare $(x+\dfrac{2}{x})^8$ to $(a+b)^n$ , we get n=8 which is even .

Since , the middle term in any binomial expansion = $(\dfrac{n}{2}+1)^{th}\text{term}$

i.e. Middle term  = $(\dfrac{8}{2}+1)^{th}\text{term}=5^{th}\text{term}$

∵ (r+1) th term of binomial = $T_{r+1}=^nC_ra^{n-r}b^r$

Then, 5th term of $(x+\dfrac{2}{x})^8$  will be :-

$T_5=T_{4+1}=^8C_4(x)^{8-4}(\dfrac{2}{x})^4\\\\=\dfrac{8!}{4!(8-4)!}x^4\times\dfrac{16}{x^4}\\\\=70\times16=1120$

Hence, middle term of $(x+\dfrac{2}{x})^8$ =1120