Alternating sums concerning multiplicative arithmetic functions

László Tóth

We deduce asymptotic formulas for the alternating sums ${\sum }_{n\le x}(-1{)}^{n-1}f(n)$ and ${\sum }_{n\le x}(-1{)}^{n-1}\frac{1}{f(n)}$, where $f$ is one of the following classical mult…