Use the following provided fraction in term of x ------2/x(x+1)(x+2)
to find the answer of 1/1.2.3+1/2.3.4+1/3.4.5+...+1/8.9.10
Maths question F.4.
2010-03-25 2:50 am
回答 (1)
2010-03-25 3:30 am
✔ 最佳答案
Since 2 / [x(x+1)(x+2)] = [(x+2) - x] / [x(x+1)(x+2)]
= 1 / [x(x+1)] - 1 / [(x+1)(x+2)]
So
2/1.2.3 + 2/2.3.4 + 2/3.4.5 +...+ 2/8.9.10
= (1/1*2 - 1/2*3) + (1/2*3 - 1/3*4) + (1/3*4 - 1/4*5) + (1/4*5 - 1/5*6)
+ (1/5*6 - 1/6*7) + (1/6*7 - 1/7*8) + (1/7*8 - 1/8*9) + (1/8*9 - 1/9*10)
= 1/1*2 - 1/9*10
= 1/2 - 1/90
= 22/45
So
the answer of 1/1.2.3+1/2.3.4+1/3.4.5+...+1/8.9.10 = (1/2)(44/90) = 11/45
收錄日期: 2021-04-21 22:10:41
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