已知an=1/2n(n+1),a1=1,求sn.急用!

网友回答

2an=1/n(n+1)=1/n-1/(n+1)
2S=2a1+2a2+2a3+.+2an
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)...+(1/n-1/(n+1))
=1-1/(n+1)
S=n/(2n+2)
======以下答案可供参考======
供参考答案1:
sn=1/2(1-1/2+1/2-1/3+......+1/n-1/n+1)
=1/2-1/(n+1)
供参考答案2:
用数学归纳法做
供参考答案3:
an=(1/2)n(n+1)=1+2+...+n
Sn=1+(1+2)+...+(1+2+...+n)
=1*n+2*(n-1)+...+n*[n-(n-1)]
=n*(1+2+...+n)-[2+3*2+...+n(n-1)]
=(1/2)n^2 *(n+1)-2[1+3+...+(1/2)n(n+1)]+n(n+1)
=(1/2)n^2 *(n+1)-2Sn+n(n+1)
Sn=