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1/6x7+1/7x8+1/8x9+.+1/100x101=1/?
题目详情
1/6x7+1/7x8+1/8x9+.+1/100x101=1/?
▼优质解答
答案和解析
1/[x(x+1)]=1/x-1/(x+1)
1/6x7+1/7x8+1/8x9+.+1/100x101
=1/6-1/7+1/7-1/8+1/8-1/9+.+1/100-1/101
=1/6-1/101
=95/101
1/6x7+1/7x8+1/8x9+.+1/100x101
=1/6-1/7+1/7-1/8+1/8-1/9+.+1/100-1/101
=1/6-1/101
=95/101
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