How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits?

Question

How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits? This is in relation to radioactive decay for those that are wondering, thank you for your help and time! <3 :) 

Answer 1

If the 2nd equation

dN/dt = -λN

is correct, then the 1st equation

−λ△t= (N(t+△t)−N(t)) / (△t)

CANNOT be correct.  λ must have units of time^-1, so the left side of the 1st equation is dimensionless.  The right side has units of amount/time. The left and right sides are different physical quantities. They cannot be equal.