bolton8l

bolton8l

Answered

2022-10-08

Proof that lim ( ϑ ( x ) x ) 0 ? ?

Do you have a similar question?

Recalculate according to your conditions!

Want to know more about Two-wayTables?

Answer & Explanation

Farbwolkenw

Farbwolkenw

Expert

2022-10-09Added 6 answers

lim x (   p x   log p x ) does not exist. We can prove it by contradiction.
If lim x (   p x   log p x ) exists, then
0 = lim x (   p ( x + 1 ) log p ( x + 1 ) ) lim x (   p x log p x ) = lim x   x < p ( x + 1 ) log p 1
It means that lim x   x < p ( x + 1 ) log p = 1
If there is a prime in ( x , x + 1 ], then x < p ( x + 1 ) log p > log x, if there is no prime in ( x , x + 1 ], then x < p ( x + 1 ) log p = 0, so lim x   x < p ( x + 1 ) log p cannot exist, it contradicts with the previous, so lim x (   p x   log p x ) cannot exist.

Still Have Questions?

Ask Your Question

Free Math Solver

Help you to address certain mathematical problems

Try Free Math SolverMath Solver Robot

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?