数列{an}的前n项和为Sn,an=1/n(n+1),求S5.
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数列{an}的前n项和为Sn,an=1/n(n+1),求S5.
数列{an}的前n项和为Sn,an=1/n(n+1),求S5.
数列{an}的前n项和为Sn,an=1/n(n+1),求S5.
an=1/[n(n+1)]=1/n-1/(n+1)
Sn=(1-1/2)+(1/2-1/3)+……+[1/n-1/(n+1)] n>=1且为整数
=1-1/(n+1)
当n=5时 Sn=1-1/6=5/6
an=1/[n(n+1)]=1/n -1/(n+1)
S5=a1+a2+a3+a4+a5
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
补充:
Sn=a1+a2+...+an
=1/1-1/2+1/2-1/3+...+1/n -1/(n+1)
=1- 1/(n+1)
=n/(n+1)
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