Question 3: Find the limit of the convergent of the following sequences:
Solution
(a) 
Cancelling ‘n’, 
Answer
(b) 
Answer
(c) 
Cancelling ‘n’ over and below,
Answer
(d).
Now let
Therefore,
Put the value of y,
Answer
L’Hospital Rule
When the limit is of the form 0/0 or ∞/∞ etc, this is usually called the indeterminate form. In such cases the limit can’t be determined directly. So we use some mathematical trick to make the limit “determinate or definable”. In the previous sections we simplified such problems.
L’Hospital rule can be considered one such trick, too!. It states that in case ‘a’ is a real number or infinity, and
then, 
(L’Hospital is pronounced L’Hopital)
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