Thread: prime series......

I was just trying to solve the problem from a book by David M. Burton.

If any help in formulating a solution can be rendered, I shall be highly obliged.



thanks
kaka

To repeat what I put in your last post.

If you want people to take the time to solve your questions please make the effort to write out the question in full, and not just provide a download link.

Thankyou

Originally Posted by craig

To repeat what I put in your last post.

If you want people to take the time to solve your questions please make the effort to write out the question in full, and not just provide a download link.

Thankyou

I think providing a PDF file is fine; I, on the other hand, would never open an unknown .doc file...

Tonio

Originally Posted by kaka1988

Let $\displaystyle p_n $ denote the $\displaystyle n^{th} $ prime. For $\displaystyle n>3 $, show that $\displaystyle p_n<p_1+p_2+p_3+\ldots+p_{n-1} $.

Prove this by induction. I'll leave the base case of $\displaystyle n=4 $ to you.

Now suppose $\displaystyle p_n<p_1+p_2+p_3+\ldots+p_{n-1} $, then $\displaystyle p_n+p_n<p_1+p_2+p_3+\ldots+p_{n-1}+p_n $.

But Bertrand's Postulate tells us that $\displaystyle p_{n+1}<2p_n $.

So we get $\displaystyle p_{n+1}<2p_n<p_1+p_2+p_3+\ldots+p_n $, which proves the claim.

Actually I don't know how to use [tex] tags, that's why i had to use a .doc file to post my question.

Kindly guide me.


thanks kaka

Originally Posted by kaka1988

Actually I don't know how to use [tex] tags, that's why i had to use a .doc file to post my question.

Kindly guide me.


thanks kaka

Read "LaTeX Help" in the section "Math Resources"

Tonio