I think (i) is 0 and (ii) is 1.... but i am only coming to these answers intuitively.... is there a way to verify them?
What are the limits of the follwing sequences as n tends towards infinity?
(i)
(ii)
(iii)
(iv)
I had a go at (iv) and got an answer 1/4....
Im not really sure how to do the others, they are part of a past exam paper and there is no mark scheme, so when i get to an answer im not sure if it is right or not!
Using intuition is a first step to solving problems , then you may solve them by following your intuition .
For example , for question (i) , intuitively it is zero , we can do something to prove it zero . We know is zero so can we do something to rewrite the limit in this form ?
.
Multiply numerator and denominator by :
.
This is the same as . The numerator is 1 while the denominator gets bigger and bigger without bound.(ii)
Probably the simplest thing to do is use L'Hopital's rule- 100 times!(iii)
If you were to multiply out the numerator, the leading term would be 6n^3. Doing the same in the denominator the leading term would be 144n^4. Divide both numerator and denominator by .(iv)
I had a go at (iv) and got an answer 1/4....
Im not really sure how to do the others, they are part of a past exam paper and there is no mark scheme, so when i get to an answer im not sure if it is right or not!