In 
 The index is (2n - 1), which is odd.
∴        There are two middle terms.
                 

                 

                  

Sum of co-efficients of the two middle terms = 
                                                                                (∵ )
                                                                                                   ...(i)
In 
The index is 2n, which is even.
∴ There is only one middle term.             
                            
∴                                                                              ...(ii)

From (i) and (ii), we have the sum of co-efficients of two middle terms in the expansion of  is equal to the co-efficient of a single middle term in the expansion of