Real Sequence/Examples/Half of (x (n-1) + 2 over x (n-1))

Examples of Real Sequence

The first few terms of the real sequence:

$S = \sequence {a_n}_{n \mathop \ge 1}$

defined as:

$a_n = \begin {cases} 2 & : n = 1 \\ \dfrac 1 2 \paren {x_{n - 1} + \dfrac 2 {x_{n - 1} } } & : n > 1 \end {cases}$

are:

$2, \dfrac 3 2, \dfrac {17} {12}, \dfrac {577} {408}, \dotsc$

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 4$: Convergent Sequences: $\S 4.3$: Examples: $\text{(v)}$