# Spot the mistake

Calculus Level 1

Here's my attempt at proving that $$2=1$$. In which step did I first commit a flaw in my logic?

\begin{align} 1^2&=1\\ 2^2&=2+2&\text{(2 times)}\\ 3^2&=3+3+3&\text{(3 times)} \end{align}

Step 1: For any positive integer:

$x^2=x+x+\cdots+x\quad\quad\text{(x times)}$

Step 2: Now, differentiating with respect to $$x$$:

$2x=1+1+\cdots+1\text{(x times)}.$

Step 3: Summing this up, we get

$2x = x.$

Step 4: Dividing by $$x$$, we get

$2 = 1.$

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