# Give the examples of: a) Harmonic series b) Alternating harmonic series

Give the examples of:
a) Harmonic series
b) Alternating harmonic series
c) Geometric series

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Maciej Morrow
a) Harmonic series is the divergent infinite series:
$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}}={1}+\frac{{1}}{{2}}+\frac{{1}}{{3}}+\frac{{1}}{{4}}+\frac{{1}}{{5}}+…$$
b) Alternating harmonic series
It’s converging series, which converge to $$\displaystyle{{\ln}_{{2}}}$$
$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{\left(-{1}\right)}^{{{n}–{1}}}}{{n}}={\ln{{2}}}$$
$$\displaystyle{1}+\frac{{1}}{{3}}+\frac{{1}}{{5}}+…={2.021}$$
c) Geometric series is a series with a constant ratio between successive terms:
$$\displaystyle\frac{{1}}{{2}}+\frac{{1}}{{4}}+\frac{{1}}{{8}}+\frac{{1}}{{16}}+…$$