设连续函数f(x)在[1,+∞)单调减少,且f(x)>0,若un=nk=1f(k)-∫n1f(x)dx,证明:limn→∞un

设连续函数f(x)在[1,+∞)单调减少,且f(x)>0,若un=nk=1f(k)-∫n1f(x)dx,证明:limn→∞un存在.