观察:1/(1X2)=1-(1/2),1/(2X3)=(1/2)-(1/3),1/(3X4)=(1/3)-(1/4).请写出第n个等式;并证明它.(谢谢啦!)
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![观察:1/(1X2)=1-(1/2),1/(2X3)=(1/2)-(1/3),1/(3X4)=(1/3)-(1/4).请写出第n个等式;并证明它.(谢谢啦!)](/uploads/image/z/2580200-8-0.jpg?t=%E8%A7%82%E5%AF%9F%EF%BC%9A1%2F%EF%BC%881X2%29%3D1-%281%2F2%29%2C1%2F%282X3%29%3D%281%2F2%29-%281%2F3%29%2C1%2F%283X4%29%3D%281%2F3%29-%281%2F4%29.%E8%AF%B7%E5%86%99%E5%87%BA%E7%AC%ACn%E4%B8%AA%E7%AD%89%E5%BC%8F%EF%BC%9B%E5%B9%B6%E8%AF%81%E6%98%8E%E5%AE%83.%EF%BC%88%E8%B0%A2%E8%B0%A2%E5%95%A6%21%EF%BC%89)
观察:1/(1X2)=1-(1/2),1/(2X3)=(1/2)-(1/3),1/(3X4)=(1/3)-(1/4).请写出第n个等式;并证明它.(谢谢啦!)
观察:1/(1X2)=1-(1/2),1/(2X3)=(1/2)-(1/3),1/(3X4)=(1/3)-(1/4).
请写出第n个等式;并证明它.(谢谢啦!)
观察:1/(1X2)=1-(1/2),1/(2X3)=(1/2)-(1/3),1/(3X4)=(1/3)-(1/4).请写出第n个等式;并证明它.(谢谢啦!)
第n个等式:
1/n*(n+1)=1/n-1/(n+1)
证明:
1/n-1/(n+1)=(n+1-n)/n(n+1)=1/n(n+1)
1/(n*(n+1))=((n+1)-n)/(n*(n+1))=1/n-1/(n+1)