设an=1+1/2+1/3+...1/(3n-1),(n∈N+)则a(n+1)-an等于
问题描述:
设an=1+1/2+1/3+...1/(3n-1),(n∈N+)则a(n+1)-an等于
答
注意到an=1+1/2+1/3+...+1/(3n-1)
它的分母是连续自然数
所以a(n+1)=1+1/2+1/3+...+1/(3n-1)+1/(3n)+1/(3n+1)+1/(3n+2)
∴a(n+1)-an=1/(3n)+1/(3n+1)+1/(3n+2)