作业帮求和：1：Sn=1/1*3+1/2*4+1/3*5+.+1/n*(n+2) 2：Sn=1/1*2+1/2*3+1/3*4
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/22 07:13:50
求和：1：Sn=1/1*3+1/2*4+1/3*5+.+1/n*(n+2) 2：Sn=1/1*2+1/2*3+1/3*4+.+1/n(n+1)
1：Sn=1/1*3+1/2*4+1/3*5+.+1/n*(n+2)
= 1/2*(1-1/3) + 1/2*(1/2 - 1/4) + ...+ 1/2*(1/n - 1/(n+2))
= 1/2 ( 1+ 1/2 - 1/(n+1) - 1/(n+2))
2：Sn=1/1*2+1/2*3+1/3*4+.+1/n(n+1)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/n - 1/(n+1)
= 1- 1/(n+1)
= n / (n+1)
= 1/2*(1-1/3) + 1/2*(1/2 - 1/4) + ...+ 1/2*(1/n - 1/(n+2))
= 1/2 ( 1+ 1/2 - 1/(n+1) - 1/(n+2))
2：Sn=1/1*2+1/2*3+1/3*4+.+1/n(n+1)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/n - 1/(n+1)
= 1- 1/(n+1)
= n / (n+1)
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