binomial

prove that 100!=250(1．3．5．．．99)．50!
100! = 1．2．3．….. ．99．100
= (1．3．5．…. ．99)(2．4．6．……．100)
= (1．3．5．…. ．99)[(1．2)．(2．2)．(2．3)．……．(2．50)]
= (1．3．5．…. ．99)[(1．2．3．…．50)．(2．2．2….2)] à(50個2相乘)
= (1．3．5．…. ．99)．50!．250
= R.H.S
所以這式成立。