关于二项式定理的.C10取9 + C11取9 + C12取9 + ...+ C19取9 = 结果是C20取10 -1吧还是+1怎么_数学解答

关于二项式定理的.
C10取9 + C11取9 + C12取9 + ...+ C19取9 = 结果是C20取10 -1吧还是+1
怎么算的?把步骤写下来,

人气：386 ℃　时间：2020-05-28 09:10:14

解答

Cn取m+Cn取m+1=Cn+1取m+1(公式)
则,C10取9 + C11取9 + C12取9 + ...+ C19取9
=C10取10+C10取9 + C11取9 + C12取9 + ...+ C19取9 -C10取10
=C11取10+C11取9 + C12取9 + ...+ C19取9 -1
=C12取10+ C12取9 + ...+ C19取9 -1
=C13取10+C13取10+.+ C19取9 -1
=.=C19取10+ C19取9 -1
=C20取10 -1