Thread: help proof limit n to infinity (n+1)^1/3 - n (1/3)

Please help to shed some light on how to proof this. This is a home work problem from my real analysis class.

thanks

Originally Posted by MaxJasper

Try (n+1)/n = 1+1/n

How do I do that? I can't find a common factor that will turn it into the form (n+1). I have tried to multiply with [(n+1)^1/3 + n^(1/3)] / [(n+1)^1/3 + n^(1/3)] . But can't get rib of the power.

Originally Posted by kanli

Please help to shed some light on how to proof this. This is a home work problem from my real analysis class.

thanks

Is this supposed to be ?

Originally Posted by kanli

Please help to shed some light on how to proof this. This is a home work problem from my real analysis class.

thanks

Hint: Use the difference of cubes formula



This gives the limit

thank you very much. I solved the problem.