Real Sequence/Examples/Arbitrary Sequence 2

Examples of Real Sequence

The recurrence relation:

$s_n = \begin {cases} 1 & : n = 1 \\

0 & : n = 2 \\ \dfrac {s_{n - 2} + s_{n - 1} } 2 & : n > 2 \end {cases}$

defines a real sequence whose first few terms are:

$1, 0, \dfrac 1 2, \dfrac 1 4, \dfrac 3 8, \dfrac 5 {16}, \dotsc$

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $1$: Review of some real analysis: $\S 1.2$: Real Sequences: Example $1.2.1 \, \text {(f)}$