The sum of the first n integers is , not
The induction should show that your theroem is false.
Since it doesn't hold for 1, that's a clue.
What is wrong with this "proof"?
"Theorem" For every positive integer n,
Basic step : The formula is true for n = 1
Inductive Step: Suppose that . Then . By the inductive hypothesis, , completing the inductive step.
What I have found wrong is the basic step actually doesn't hold true for n = 1. But I cant find any other mistakes