If |a1|<=1 and |an - an-1|<=1 , then |an|<=n

I started with |ak - ak-1|<=1 and used the triangle inequality but I get two things that are grater than or equal to |an - an-1| ! If I assume that |ak| + |ak-1|<=1 and then take for granted that if thats true then |ak+1| + |ak|<=1 then I can proove the whole thing, but I donīt really think Iīm doing it right. Please help me! Its going to appear in a test... Thanks