Show that 1+1/2+1/3+1/4+...is infinite.
(In reply to
One proof out of many by JLo)
Yours is the only proof I know of. This is equivalent but may be clearer.
Note that the series can be broken up by powers of two:
1 + 1/2 + 1/3+1/4 + 1/5+1/6+1/7+1/8 + 1/9+...+1/16 + ...
Which is greater than
1 + 1/2 + 1/4+1/4 + 1/8+1/8+1/8+1/8 + 1/16+...+1/16 + ... = 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...
An expression that is clearly infinite. If our expression is greater than this it must also be infinite.
|
|
Posted by Jer
on 2006-10-03 11:00:20 |
re: One proof out of many
