谁能替我通俗易懂的解释下高中数列里的裂项相消啊?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/08 17:30:35
谁能替我通俗易懂的解释下高中数列里的裂项相消啊?谁能替我通俗易懂的解释下高中数列里的裂项相消啊?谁能替我通俗易懂的解释下高中数列里的裂项相消啊?全部展开收起1/1x2+1/2x3+1/3x4+1/4x

谁能替我通俗易懂的解释下高中数列里的裂项相消啊?
谁能替我通俗易懂的解释下高中数列里的裂项相消啊?

谁能替我通俗易懂的解释下高中数列里的裂项相消啊?

收起

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6=5/6
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
=1/2(1-1/3)+...

全部展开

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6=5/6
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/12)
=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/12)
=1/2(1-1/12)
=1/2x11/12
=11/24

收起