已知数列an满足an=1/n(n+1)。求前n项和sn
an=1/n(n+1)
=1/n - 1/(n+1)
故Sn=a1+a2+...+an
=(1-1/2)+(1/2-1/3)+...+[1/n- 1/(n+1)]
=1-1/(n+1)
=n/(n+1)
a(n)
=1/[n(n+1)]
=1/n-1/(n+1)
S(n)
=a(1)+a(2)+a(3)+......+a(n)
=(1-1/2)+(1/3-1/4)+(1/4-1/5)+......+[1/n-1/(n+1)]
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.....+1/n-1/(n+1)
=1-1/(n+1)
=(n+1)/(n+1)-1/(n+1)
=n/(n+1)
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