How do I know when mathematical sequences are bounded?

Franzi576ByFranzi576

How do I know if a sequence is bounded or not? I haven't found any explanation online. For an upper or lower bound, all values ​​must be greater or less than a certain number, but how do I figure that out?

Are all arithmetic sequences bounded either above or below?

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Schachpapa
Schachpapa
1 year ago

Are all arithmetic consequences limited either up or down?

Yeah.

For d>0, the sequence is limited by the initial member downwards (after this only goes up), for d <0, the sequence is limited by the initial member upwards (after this only goes down).

For an upper or lower limit, all values must be larger or smaller than a certain number, but do I come to that?

Often enough, the burial is not obvious. One looks at the episode, has a presumption and must prove it with the appropriate methods. If you cannot see or not prove the limitation, it does not necessarily mean that the result is not limited. It is also necessary to prove that (unlimitedness).

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Littlethought
Littlethought
1 year ago

An arithmetic sequence is sufficient to form x(i) = a + (i – 1 ) * d ;

If 0 < d, then the sequence is strictly monotonous and a is the minimum of the sequence. Analogue to d < 0 .

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