Question

     i.       Find the first 3 terms, in ascending powers of , in the expansion of .

The coefficient of  in the expansion of  is 95.

   ii.       Use the answer to part (i) to find the value of the positive constant .

Solution

i.
 

Expression for the Binomial expansion of  is:

In the given case:

Hence;

ii.
 

To evaluate the expansion of  we can substitute  in the equation obtained in (i);

According to the given condition, the coefficient of  in the expansion of  is
95. Therefore;

Since we are required to find the value of the positive constant ;