一條簡單計算題

2009-01-11 8:51 pm
從2 / [(k + 1)(k + 2)] + [ 1 – 2 / (k + 3)]計到 2 / [(k + 2)(k + 3)]

回答 (2)

2009-01-12 4:11 am
✔ 最佳答案
Let k=1
LHS=2/[(2)(3)]+[1-2/4]
=1/3+1/2
=5/6
RHS=2/[(3)(4)]
=1/6
LHS=/=RHS

Let k=2
LHS=2/[(3)(4)]+[1-2/5]
=1/6+3/5
=23/30
RHS=2/[(4)(5)]
=1/10
LHS=/=RHS

∴It is not an equality actually
2009-01-11 11:02 pm
This is not an equality
consider k=1
LHS=2/[(2)(3)]+[1-2/4]=1/3+1/2=5/6
RHS=2/[(3)(4)]=1/6=/=LHS

consider k=2
LHS=2/[(3)(4)]+[1-2/5]=1/6+3/5=23/30
RHS=2/[(4)(5)]=1/10=/=LHS

∴It is not an equality actually


收錄日期: 2021-04-27 14:19:55
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