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Succession

succession is called a function whose domain is the set of natural numbers.

to denote the nth element of the sequence is written n instead of f (n).

Example:

_to n = 1 / n

_to 1 = 1, 2 = 1 / 2 to 3 = 1 / 3, a ₄ = 1 / 4, ...

Succession monotone increasing

A sequence is monotone increasing if it is true that for all natural n to _{n n +1} <= a (a _{1 2} <= a ₃ <= ... <= a n). <= a

Example:

_to n = n is monotone increasing.

_to 1 = 1, 2 = 2, 3 = 3, 4 = 4, ...