1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10这道题怎么做
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![1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10这道题怎么做](/uploads/image/z/378949-13-9.jpg?t=1%2F2%2B1%2F2%2A3%2B1%2F3%2A4%2B1%2F4%2A5%2B1%2F5%2A6%2B1%2F6%2A7%2B1%2F7%2A8%2B1%2F8%2A9%2B1%2F9%2A10%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E5%81%9A)
1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10这道题怎么做
1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10这道题怎么做
1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10这道题怎么做
1 = 1 - 1/2 1/(2×3) = 1/2 - 1/3 ……………………………… 1/[n(n + 1)] = 1/n - 1/(n + 1) 原式= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ……………… + 1/9 - 1/10 = 1 - 1/10 = 9/10