OK: denotes the prime. For , show that

the hint was to use induction and Bertrand's conjecture

ok: so the answer is in the book, but its not helpful b/c I don't get one jump

so they do this:

So for n=4, , which is true.

Assume for some k,

By Bertrand, there exists a prime between and

Here is where I'm lost: they go from there to ,

thus proving that statement is true for

How? *so confused*