1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算1/1×3+1/3×5+1/5×7+.+1/2013×2015=多少
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 19:54:35
![1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算1/1×3+1/3×5+1/5×7+.+1/2013×2015=多少](/uploads/image/z/13318406-62-6.jpg?t=1%2F1%C3%973%3D1%2F2%EF%BC%881-1%2F3%EF%BC%89%EF%BC%9B1%2F3%C3%975%3D1%2F2%EF%BC%881%2F3-1%2F5%EF%BC%891%2F5%C3%977%3D1%2F2%281%2F5-1%2F7%29%E7%94%B1%E6%AD%A4%E8%AE%A1%E7%AE%971%2F1%C3%973%2B1%2F3%C3%975%2B1%2F5%C3%977%2B.%2B1%2F2013%C3%972015%3D%E5%A4%9A%E5%B0%91)
1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算1/1×3+1/3×5+1/5×7+.+1/2013×2015=多少
1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算
1/1×3+1/3×5+1/5×7+.+1/2013×2015=多少
1/1×3=1/2(1-1/3);1/3×5=1/2(1/3-1/5)1/5×7=1/2(1/5-1/7)由此计算1/1×3+1/3×5+1/5×7+.+1/2013×2015=多少
裂项法:
1/1×3+1/3×5+1/5×7+.+1/2013×2015
=1/2×(1-1/3+1/3-1/5+1/5-1/7+……+1/2013-1/2015)
=1/2×(1-1/2015)
=1/2×2014/2015
=1007/2015