1/1+1/3+1/6+1/10+.1/45= 请简算 答案为9/5
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1/1+1/3+1/6+1/10+.1/45= 请简算 答案为9/5
![1/1+1/3+1/6+1/10+.1/45= 请简算 答案为9/5](/uploads/image/z/11062994-50-4.jpg?t=1%2F1%2B1%2F3%2B1%2F6%2B1%2F10%2B.1%2F45%3D+%E8%AF%B7%E7%AE%80%E7%AE%97+%E7%AD%94%E6%A1%88%E4%B8%BA9%2F5)
=1/1+1/(1+2)+1/(1+2+3)+……+1/(1+2+3+4+5+6+7+8+9)
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/(9*10)
=2*(1/1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10)
=2*(1/1-1/10)
=2*(9/10)
=9/5
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/(9*10)
=2*(1/1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10)
=2*(1/1-1/10)
=2*(9/10)
=9/5