Question

pls help me out with correct answer to question and give step by step explaination ​

Answer 1

Answer:

OPTION D

Step-by-step explanation:

The number of terms in $(x+1+\dfrac{1}{x})^n$ is 301 .

The above can be written as :

$(x+\dfrac{1}{x}+1)^n\\\\\bf{Let\:x+\dfrac{1}{x}\:be\:a}$

So the equation becomes $(a+1)^n$

Given $(a+1)^n$ has 301 terms .

The value of n here determines the number of terms .

The value of n can be 150 only because :-

In an expansion like $(x+1)^n$ the number of terms have power from 0 to 2 n and hence contains 2 n + 1  terms .

There are a few exceptions however .

Hence 2 n + 1 = 301

⇒ 2 n = 300

⇒ n = 300/2

⇒ n = 150

The number of terms will be 150 .

Hence 149 is the answer because it is greater than 150 .

Answer 2

ANSWER

plz, refer to the attachment for the answer here.

The correct option us (D).

But remember that =>

-The value if n is 150 only.

-In an expansion like$(x+1)^{n}$,the number of terms have power from 0 to 2 n and hence contains (2n + 1) terms.