设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=
问题描述：
设an=1+1/2+1/3+1/4+...+1/3n-1(n∈N*),则a(n+1)-an=
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答
a(n+1) = 1+1/2+1/3+.+1/(3n-1)+...+1/[3(n+1)-1]= 1+1/2+1/3+.+1/(3n-1)+...+1/(3n+2)= 1+1/2+1/3+.+1/(3n-1)+1/3n+1/(3n+1)+1/(3n+2)an = 1+1/2+1/3+.+1/(3n-1)a(n+1) - an = 1/3n + 1/(3n+1) + 1/(3n+2)