How would you do this ? (1 Viewer)

[An0nyM0usUseR455]

I got the RHS of the inequality just dont understand why 1 is less than nth root of n. Should it not be less than or equal to?

 

[tywebb]

Yes I think it should be less than or equal to, equal in the case of n=1.

If you allow n to be a real number you can get it to be less than 1 but the maximum is so for positive integers the maximum is and minimum is 1. So a tighter bound for positive integers is

You can see it more clearly in the graph of

Range for real is

Range for positive integers is

 

[tywebb]

So to do the actual question:

a.








Hence by the principle of mathematical induction, for all positive integers

b.

 

[An0nyM0usUseR455]

So to do the actual question:

a.








Hence by the principle of mathematical induction, for all positive integers

b.

Thanks bro appreciate it !!!

I applied the same steps as u, was just confused why there was no equal sign but I am glad you agree with me !!!

Have a great night