prime series......

**kaka1988** · Apr 25th 2010, 01:37 AM

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

**craig** · Apr 25th 2010, 02:33 AM

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

**tonio** · Apr 25th 2010, 03:26 AM

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

**chiph588@** · Apr 25th 2010, 06:35 PM

Originally Posted by kaka1988

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

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

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

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

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

**kaka1988** · Apr 26th 2010, 10:50 PM

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

**tonio** · Apr 27th 2010, 03:37 AM

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

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