Binomial Expansion Formula

Step 1: Understanding the Problem

We are given that:

This means that represents the coefficient of in the expansion of .

Step 2: General Term of the Expansion

From the binomial theorem, the general term is:

So, the coefficient of is:

Step 3: Behavior of Coefficients

We need to find which is the largest among .

To do this, consider the ratio:

Simplify:

Step 4: Condition for Increasing Sequence

If , the sequence increases; if less than 1, it decreases.

Step 5: Identifying the Maximum

Thus, the coefficients increase up to and then start decreasing after

Therefore, the largest coefficient occurs at .

Final Answer

The value of is:

r = 6