Exercise · ZW-CAUCHY-SEQUENCE-003 · ★☆☆ Basic
If \(a_n=1/n\), compute \(|a_{10}-a_{20}|\).
Choose one option.
Show answer
- D. \(\tfrac1{20}\)
Explanation
We have \(\frac1{10}-\frac1{20}=\frac{2-1}{20}=\frac1{20}\).
Review the concept: Cauchy sequence
A sequence \((a_n)\) is Cauchy if, for every \(\varepsilon>0\), there is an index \(N\) beyond which any two terms are less than \(\varepsilon\) apart.
\[\forall\varepsilon>0\ \exists N:\ m,n\ge N\Rightarrow|a_m-a_n|<\varepsilon\]
More practice problems: cauchy sequence
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