3. (a) Simplify 1/n - 1/(n+1) . (b) Using (a), find the value of . (1)/(2*3) + (1)/(3*4) + 1/(4*5)+ .....+ 1/(99*100)?
回答 (1)
2016-05-20 3:56 am
a)
1/n - 1/(n+1)
=(n + 1 - n)/[n(n + 1)]
=1/[n(n + 1)].
b)
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5)+ ... + 1/(99 × 100)
=(1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ... + (1/99 - 1/100)
=1/2 - 1/100
=49/100
1/n - 1/(n+1)
=(n + 1 - n)/[n(n + 1)]
=1/[n(n + 1)].
b)
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5)+ ... + 1/(99 × 100)
=(1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ... + (1/99 - 1/100)
=1/2 - 1/100
=49/100
收錄日期: 2021-04-18 14:55:22
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