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1*2/1+2*3/1+3*4/1+4*5/1……+199*200/1简算!
题目详情
1*2/1 + 2*3/1 + 3*4/1 + 4*5/1……+ 199*200/1 简算!
▼优质解答
答案和解析
是这样的题吧：
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(199×200)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/198-1/199+1/199-1/200
=1-1/200
=199/200
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(199×200)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/198-1/199+1/199-1/200
=1-1/200
=199/200
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