perplexus.info :: Just Math : Those infinite small steps

Home > Just Math

Those infinite small steps (Posted on 2006-10-03)

Show that 1+1/2+1/3+1/4+...is infinite.

No Solution Yet Submitted by Art M

Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Another one

| Comment 5 of 8 |

Assume the sum is finite and let's call it S. Then

S=1+1/2+1/3+1/4+1/5+1/6... > 1/2+1/2+1/4+1/4+1/6+1/6...
= 2*(1/2+1/4+1/6...) = 2*S/2 = S

Follows S>S. Contradiction, therefore S is not finite.

Posted by JLo on 2006-10-03 15:33:22

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info