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i've to show (as part of a bigger assignment) that

a^n/p(n), where p is any polynomial and a>1, tends to infinity as n does. i've proved that:

a^n/n^k

does so, but i'm not sure how to extend this to a complete polynomial such as

(c1)n+(c2)n^2+(c3)n^3...

thanks for any help

NB: edited

a^n/p(n), where p is any polynomial and a>1, tends to infinity as n does. i've proved that:

a^n/n^k

does so, but i'm not sure how to extend this to a complete polynomial such as

(c1)n+(c2)n^2+(c3)n^3...

thanks for any help

NB: edited

Last edited: