Infinity Is Negative?

Calculus Level 1

I'm going to prove that \(1 + 2 + 2^2 + 2^3 + \cdots = -1 \). Is the following working correct?

Let \(A \) denote the value of \(1 + 2 + 2^2 + 2^3 + \cdots \), then

\[ \begin{eqnarray} 2A &=& 2 + 2^2 + 2^3 + 2^4 + \cdots \\ 2A + 1 &=&1 + 2 + 2^2 + 2^3 + 2^4 + \cdots \\ 2A + 1 &=&A \\ A &=&-1. \end{eqnarray} \]

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