作业帮[1\1+2]+[1\1+2+3]+[1\1+2+3+4]+...+[1\1+2+3+...+50]=
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/06 07:36:01
![[1\1+2]+[1\1+2+3]+[1\1+2+3+4]+...+[1\1+2+3+...+50]=](/uploads/image/z/10841107-67-7.jpg?t=%5B1%5C1%2B2%5D%2B%5B1%5C1%2B2%2B3%5D%2B%5B1%5C1%2B2%2B3%2B4%5D%2B...%2B%5B1%5C1%2B2%2B3%2B...%2B50%5D%3D)
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[1\1+2]+[1\1+2+3]+[1\1+2+3+4]+...+[1\1+2+3+...+50]=
[1\1+2]+[1\1+2+3]+[1\1+2+3+4]+...+[1\1+2+3+...+50]=
[1\1+2]+[1\1+2+3]+[1\1+2+3+4]+...+[1\1+2+3+...+50]=
1+2+3+..+n=n(n+1)/2 1/(1+2+3+...+n)=1/[(n(n+1)/2]=2[1/n-1/(n+1)] 所以 1/(1+2)=2(1/2-1/3) 1/(1+2+3)=2(1/3-1/4) 1/(1+2+3+.+50)=2(1/50-1/51) 所有相加有2(1/2-1/3+1/3-1/4+1/4-.-1/51) =2(1/2-1/51)=49/51