✔ 最佳答案
1-(1/2)C(n,1)+(1/3)C(n,2)-.....+((-1)^n)/(n+1))C(n,n)
= C(n+1,1)/(n+1) - C(n+1,2)/(n+1) + C(n+1,3)/(n+1) +
...+(-1)^nC(n+1,n+1)/(n+1)
= 1/(n+1) -C(n+1,0)/(n+1)
+ C(n+1,1)/(n+1) - C(n+1,2)/(n+1)
+ ...+(-1)^nC(n+1,n+1)/(n+1)
= 1/(n+1) - [1/(n+1)]{C(n+1,0)-C(n+1,1)+...+(-1)^(n+1)C(n+1,n+1)}
= 1/(n+1) - [1/(n+1)](1-1)^(n+1)
= 1/(n+1)