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

ossidianaZ 2021-08-21 Answered
Give the examples of:
a) Harmonic series
b) Alternating harmonic series
c) Geometric series

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Expert Answer

Maciej Morrow
Answered 2021-08-22 Author has 4966 answers
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:
\(\displaystyle\frac{{1}}{{2}}+\frac{{1}}{{4}}+\frac{{1}}{{8}}+\frac{{1}}{{16}}+…\)
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