Binomial Expansion

The binomial expansion of is given by:
The coefficients of the terms are the binomial coefficients .
Step 1:
The sum of the coefficients of the terms for is required.
Step 2:
The sum of the coefficients of the expansion is the value of the expression when :
Step 3:
The sum of the first 40 coefficients is the sum for to , and the sum of the last 40 coefficients is
given by:
Using symmetry in the binomial coefficients, the sum of the last 40 coefficients is equal to .