Freemaths.us

                     

Exercise 18: Calculate the limit .
Solution: We divide numerator and denominator of the sequence of geometric with the highest quotient appearing in the denominator.  We divide numerator and denominator by 5ⁿ. We have

 

The sequences are convergent to 0, as they are geometric sequences  with quotients  .

We use the theorem: If  a sequence has limit  a, and a sequence has limit b ( where ), then

 a) , 

 b)  , for  .

We have

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