根据1-1/2=1/(1×2);1/2- 1/3=1/(2×3)······,用简便方法计算下列算式:1/(1×2)+1/(2×3)+1/(3×4)+········+1/(9998×9999)+1/(9999×10000).另:所以请各位在解答的时候,尽量说说为什

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 00:55:09
根据1-1/2=1/(1×2);1/2- 1/3=1/(2×3)······,用简便方法计算下列算式:1/(1×2)+1/(2×3)+1/(3×4)+········+1/(9998×9999)+1/(9999×10000).另:所以请各位在解答的时候,尽量说说为什

根据1-1/2=1/(1×2);1/2- 1/3=1/(2×3)······,用简便方法计算下列算式:1/(1×2)+1/(2×3)+1/(3×4)+········+1/(9998×9999)+1/(9999×10000).另:所以请各位在解答的时候,尽量说说为什
根据1-1/2=1/(1×2);1/2- 1/3=1/(2×3)······,用简便方法计算下列算式:1/(1×2)+1/(2×3)+1/(3×4)+········+1/(9998×9999)+1/(9999×10000).
另:所以请各位在解答的时候,尽量说说为什么要这么做,在这里先谢谢了.

根据1-1/2=1/(1×2);1/2- 1/3=1/(2×3)······,用简便方法计算下列算式:1/(1×2)+1/(2×3)+1/(3×4)+········+1/(9998×9999)+1/(9999×10000).另:所以请各位在解答的时候,尽量说说为什
1/(1×2)+1/(2×3)+1/(3×4)+········+1/(9998×9999)+1/(9999×10000)
=(1-1/2)+(1/2- 1/3)+(1/3-1/4)+········+(1/9998-1/9999)+(1/9999-1/10000)
=1-1/2+1/2- 1/3+1/3-1/4+········+1/9998-1/9999+1/9999-1/10000
=1-1/10000
=9999/10000
先根据题中的1-1/2=1/(1×2);1/2- 1/3=1/(2×3)······,把算式展开.后面就可以吧中间抵消,就好算了,呵呵