Find Limit: Where Limit ('k' approaches Infinity)   [ k/(k+1) ]^k  ?Problem is how to simplify the algebraic expression so that its limit can be calculated !!

Expert Answers
thilina-g eNotes educator| Certified Educator


We can modify the expression inside the bracket to evaluate this. Divide both numerator and denominator by k.


This gives,


When we take the limit of this, the expression inside the bracket approaches to `(1/(1+0))` which is 1. Any power of 1, no matter how big is the power it will 1 or close to one. Therefore the given limit approaches to 1.

`lim_(k-gtoo)(1/(1+1/k))^k = 1`



`lim_(k-gtoo)(k/(k+1))^k = 1`