Infinity Is Negative?

Calculus Level 1

I'm going to prove that 1+2+22+23+=11 + 2 + 2^2 + 2^3 + \cdots = -1 . Is the following working correct?

Let AA denote the value of 1+2+22+23+1 + 2 + 2^2 + 2^3 + \cdots , then

2A=2+22+23+24+2A+1=1+2+22+23+24+2A+1=AA=1. \begin{aligned} 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{aligned}

×

Problem Loading...

Note Loading...

Set Loading...