So starting at a certain value N in the sequence, when you take the infinite sum of the inequality an and an+1 would tend to positive infinity along with bn+1 but I can't tie an argument together to actually prove the result.
Homework Statement
Suppose an and bn are sequences where bn is increasing and approaching positive infinity. Assume that lim n->∞ [ ( an+1 - an ) / ( bn+1 - bn) ]= L, where L is a real number. Prove that lim n->∞ [ an / bn ] = L.
Homework Equations
Limit theorems
The Attempt at a...