Question

for every n>1, there is always a prime p: p < n < 2p.
Is that true?

Answer 1

u mean n<p<2n ?

Answer 2

yes

Answer 3

its Bertrand's postulate ...
http://en.wikipedia.org/wiki/Bertrand's_postulate

Answer 4

its true and here is the proof
http://en.wikipedia.org/wiki/Proof_of_Bertrand's_postulate

Answer 5

oh, i don't know this. But, my original problem is prove that 1/2 + 1/3 + ... + 1/n is not an integer. Can you help me?

Answer 6

this is an interesting problem though

Answer 7

@mukushla i have a confusion.
for "2" How is Bertrand's postulate true?

Answer 8

2<3<4

Answer 9

but i have taken n=2

Answer 10

.....<2<......

Answer 11

?

Answer 12

see my first reply ... jean misstated that in her/his question

Answer 13

ohhh!
thank u:)

Answer 14

jean i'v seen it before...let me provide some links for u ??

Answer 15

yes, thank you very much.

Answer 16

http://at.yorku.ca/cgi-bin/bbqa?forum=homework_help_2005;task=show_msg;msg=1682.0001

Answer 17

http://mathheaven.blogspot.in/2008/05/nth-harmonic-number-cannot-be-integer.html

Answer 18

actually this is best
http://plus.maths.org/content/perfect-harmony

Answer 19

thank you too, maheshmeghwal9

Answer 20

:D