1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=?
答案:2 悬赏:70 手机版
解决时间 2021-03-27 02:57
- 提问者网友：沉默菋噵
- 2021-03-26 07:21
1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=?
最佳答案
- 五星知识达人网友：山有枢
- 2021-03-26 08:03
解答：
∵2*【1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102】
=1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+............+1/99-1/101+1/100-1/102
=1+1/2-1/101-1/102
=(101*102+101*51-102-101)/101*102
=15250/10302
=7625/5151
∴ 1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=12=7625/10302
∵2*【1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102】
=1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+............+1/99-1/101+1/100-1/102
=1+1/2-1/101-1/102
=(101*102+101*51-102-101)/101*102
=15250/10302
=7625/5151
∴ 1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=12=7625/10302
全部回答
- 1楼网友：执傲
- 2021-03-26 08:54
1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102
=（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/100-1/102）÷2
=（1+1/2-1/101-1/102）÷2
=15250/10302÷2
=7625/5151
=（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/100-1/102）÷2
=（1+1/2-1/101-1/102）÷2
=15250/10302÷2
=7625/5151
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