Subsequence/Examples
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Examples of Subsequences
Example 1
Let $\sequence {n_r}$ be the sequence in $\N$ defined such that $n_r = r + 1$.
Then:
- $\sequence {x_{n_r} } = \sequence {x_{r + 1} } = x_2, x_3, x_4, \ldots$
Example 2
Let $\sequence {n_r}$ be defined such that $n_r = 2 r$.
Then:
- $\sequence {x_{n_r} } = \sequence {x_{2 r} } = x_2, x_4, x_6, \ldots$
Example 3
Let $\sequence {n_r}$ be defined such that $n_r = 3 r + 5$.
Then:
- $\sequence {x_{n_r} } = \sequence {x_{3 r + 5} } = x_8, x_{11}, x_{14}, x_{17}, \ldots$
Example 4
Let $\sequence {n_r}$ be defined such that $n_r = 2^r$.
Then:
- $\sequence {x_{n_r} } = \sequence {x_{2^r} } = x_2, x_4, x_8, x_{16}, \ldots$