(related to Proposition: Convergence of Alternating Harmonic Series)
Since the sequence \(\left(\frac 1n\right)\) is monotonically decreasing with \(\lim_{n\to\infty} \frac 1n=0\), it follows from the criterion for alternating infinite series that the alternating harmonic series \(\sum_{n=1}^\infty \frac {(-1)^{n-1}}n\) is convergent.