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Exercise 11: 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 exclude from brackers the highest of power variable n. We exclude n² , we get