1/1×3+1/3×5+1/5×7+…………+1/49×51和1/2×4+1/4×6+1/6×8+…………1/48×50接着 还有1/1+2 + 1/1+2+3 +……+ 1/1+2+3+……+100我明天上课用

问题描述:

1/1×3+1/3×5+1/5×7+…………+1/49×51和1/2×4+1/4×6+1/6×8+…………1/48×50
接着 还有1/1+2 + 1/1+2+3 +……+ 1/1+2+3+……+100
我明天上课用

1.原式=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/48-1/50)=1/2(1-1/50)=49/100
2.原式=2/6+2/12+2/20+……+2/n(n+1)=2(1/2-1/3+1/3-1/4+1/4-1/5+……+1/n-1/n+1)
=2(1-1/n+1)=2n/(n+1)

1/1×3+1/3×5+1/5×7+…………+1/49×51
=1/2×(1-1/3)+1/2×(1/3-1/5)+........+1/2×(1/49-1/51)
=1/2×(1-1/3+1/3-1/5+.......+1/49-1/51)
=1/2×(1-1/51)=25/51
1/2×4+1/4×6+1/6×8+…………1/48×50自己解
1/1+2 + 1/1+2+3 +……+ 1/1+2+3+……+100
=2/2×3+2/3×4+......+2/100×101
以下自己解

1/1×3+1/3×5+1/5×7+…………+1/49×51=(1-1/3+1/3-1/5+1/5-1/7+……+1/49-1/51)÷2=(1-1/51)÷2=50/51÷2=25/511/2×4+1/4×6+1/6×8+…………1/48×50=(1/2-1/4+1/4-1/6+1/6-1/8+……+1/49-1/50)÷2=(...

这题考的是2/(n)(n+2)的变形
2/(n)(n+2)=1/n -1/(n+2)
即原式=1/2(1-1/3+1/3-1/5+1/5-1/7+……-1/51)=25/51
下一题同理