- #1
5hassay
- 82
- 0
Homework Statement
What is wrong with the following calculation using infinite series?
0 = 0 + 0 + 0 + ...
0 = (1 - 1) + (1 - 1) + (1 - 1) + ...
0 = 1 - 1 + 1 - 1 + 1 - 1 + ...
0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...
0 = 1 + 0 + 0 + 0 + ...
0 = 1
Homework Equations
None.
The Attempt at a Solution
Beginning on line 4, or
0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...
an error is made. Specifically, the repeating number 0 was not completely repeated. More specifically, the -1 number of the 1 - 1 pair to make zero was not inserted, thereby making this statement invalid.
Do I have the correct idea and am I missing anything? Also, any terminology I could have used is more than welcomed!
Much appreciation!