Question

In the expansion of , the coefficient of x is 7. Find the value of the constant n and hence find the coefficient of .

Solution

Binomial Theorem states that if  is a natural number;

First we expand  .

In the given case:

Hence;

 

We will have the given product as;

We consider only the terms containing ;

We are given that coefficient of the term with x is 7. Therefore, we can equate;

Next we need to find the coefficient of .

As we have expanded the given product above;

From here we take out the term containing .

As we have found above that ;

Hence coefficient of  in the expansion of  is .