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.)

One proof out of many

| Comment 1 of 8

Wonder how many other solutions we can get for this classic. Here is mine:

S_n:=1/(2^n+1)+1/(2^n+2)+1/(2^n+3)+...+1/(2^(n+1))>=2^n*1/(2^(n+1))=1/2
therefore
1+1/2+1/3+1/4+... = 1+S_0+S_1+S_2+...>= 1+1/2+1/2+1/2+...

Edited on October 3, 2006, 8:22 am

Posted by JLo on 2006-10-03 06:30:45

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 (24)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info