高三数学问题，关于二项式定理的。

Question

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，谢谢。

Answer 1

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