数学简便运算:1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+…+1/﹙47×49﹚

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 02:50:58
数学简便运算:1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+…+1/﹙47×49﹚

数学简便运算:1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+…+1/﹙47×49﹚
数学简便运算:1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+…+1/﹙47×49﹚

数学简便运算:1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+…+1/﹙47×49﹚
1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+…+1/﹙47×49﹚
=1/2×【2/﹙1×3﹚+2/﹙3×5﹚+2/﹙5×7﹚+…+2/﹙47×49﹚】
=1/2×(1-1/3+1/3-1/5+1/5-1/7+...+1/47-1/49)
=1/2×(1-1/49)
=24/49