Calculus (3rd Edition)

This is not valid since the expanded series is: $$S_n=1+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\cdots+\frac{1}{2^n}$$ Clearly, the sum will not be zero. In other words, if the terms tend toward zero, this does not mean that they will sum to zero.