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Exercise 12: Calculate the limit  .
Solution:

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Using the model of so-called. współczynnika Newtona postaci the form of Newton's  ,  for k = 0,1,2, ..., n  , ,
we have

  

Using the definition of  factorial

n! = n * (n-1) * (n-2) * ... * 2 * 1, so n! = n * (n-1)!, therefore

 

We divide numerator and denominator by the highest power of variable n appearing in the denominator. We divide numerator and denominator by n. We have