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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

来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/07/07 12:55:30
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
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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
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
=25/51
1/2×4+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
=(1/2-1/50)÷2
=12/25÷2
=6/25
1/1+2 + 1/1+2+3 +……+ 1/1+2+3+……+100
=2*【1/2+1/2*(1+2)+1/2*(1+2++3)+……+1/2*(1+2+3+……+100)】
=2*【1-1/2+1/2-1/3+1/3-1/4+……+1/100-1/101】
=2*【1-1/101】
=2*100/101
=200/101