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We study polynomial identities of algebras over a field𝐹 of characteristic zero. Given a 𝐹 -algebra 𝐴 , one can associate a sequence 𝑐𝑛(𝐴) of non-negative integers called codimension sequence. This sequence characterize the number of polynomial identities satisfied by 𝐴 . We will discuss asymptotic behavior of the sequence 𝑐𝑛(𝐴) for distinct types of associative and nonassociative algebras A