Binomial Theorem

Since,
Coefficient of in is .

General term,


For the term independent of x, put



The term independent of x,

Given expansion is

and
According to the given condition,

Step 1: Understand the notation.
The given expression is: Where refers to the binomial coefficient .
This is the sum of binomial coefficients raised to the power of .
Step 2: Apply the binomial expansion.
The sum is a form of a binomial expansion that arises from the expansion of the binomial series: This is derived from the binomial theorem, which tells us that the sum of the coefficients (i.e., for each ) in a binomial expansion sums to .
Thus, the sum of the binomial coefficients from to is related to the total binomial sum.
Step 3: Subtract the first term.
We subtract 1 (the first term of the binomial expansion for ) since we start from :
Step 4: Conclusion.
Therefore, the sum is equal to , which corresponds to option (b).