作业帮3/1×3+3/3×5+3/5×7+...+3/19×21
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 17:28:22
3/1×3+3/3×5+3/5×7+...+3/19×21
3/1×3+3/3×5+3/5×7+...+3/19×21
3/1×3+3/3×5+3/5×7+...+3/19×21
1/n(n+2)=1/2[1/n-1/(n+2)]
3/1×3+3/3×5+3/5×7+...+3/19×21
=3(1/1*3+1/3*5+1/5*7+.+1/19*21)
=3/2(1-1/3+1/3-1/5+1/5-1/7+.+1/19-1/21)
=3/2(1-1/21)
=(3/2)*(20/21)
=10/7
此题可化为：(3/2)x(2/1x3+2/3x5+2/5x7+...+2/19x21)
=3/2x(1-1/3+1/3-1/5+1/5-1/7+....+1/19-1/21)
=3/2x(1-1/21)
=(3/2)x(20/21)=10/7
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