Chapter 9.3, Problem 26ES

The great Swiss mathematician Leonhard Euler (biography on p.66) sometimes reached incorrect conclusion in his pioneering work or infinite series. For example, Euler deduced that $\frac{1}{2}=1-1+1-1+\cdot \cdot \cdot$ and $-1=1+2+4+8+\cdot \cdot \cdot$ by substituting $x=-1\text{and}x=2$ in the formula $\frac{1}{1-x}=1+x+x^2+x^3+\cdot \cdot \cdot$

What was the problem with his reasoning?