Decreasing Sequence
Sequence in which ∀n ∈ [latex]\mathbb{R}[/latex] : x[latex]_{n}[/latex] ≥ x[latex]_{n+1}[/latex].
Examples
- The sequence {2[latex]^{–n}[/latex]} is a strictly decreasing sequence: 1, [latex]\frac{1}{2}[/latex], [latex]\frac{1}{4}[/latex], [latex]\frac{1}{8}[/latex], [latex]\frac{1}{16}[/latex], ...
- The sequence {[latex]\frac{1}{3^{n}}[/latex]} is a strictly decreasing sequence: 1, [latex]\frac{1}{3}[/latex], [latex]\frac{1}{9}[/latex], [latex]\frac{1}{27}[/latex], [latex]\frac{1}{81}[/latex], ...