The constant term in the expansion of is ______, given that only the fifth term has the maximum binomial coefficient in its expansion.
Problem 169
Official solution
Since only the fifth term has the maximum binomial coefficient in the expansion of , it implies that is an even number.
The expansion has a total of 9 terms, which means .
For , i.e., , the general term formula of its expansion is ,
Let , we find . Therefore, the constant term in the expansion is .
Hence, the answer is .
By determining from the problem statement and setting the exponent of in the general term formula of the binomial expansion to zero, we can find the value of and thus calculate the value of the constant term in the expansion.
This problem mainly examines the application of the binomial theorem, the properties of binomial coefficients, the general term formula of binomial expansion, and how to find the coefficient of a certain term in the expansion, which is a basic question.