Prove that if an infinity then an diverges Use CauchySoluti

Prove that if a_n --> infinity, then {a_n} diverges

(Use Cauchy)

Solution

By convention, if you consider a series where a(n) does not go to zero, then the series continues to add terms at a rate that never ends. This is proved by the fact that \"Terms of a convergent series go to zero\" If the series continues to add sufficiently large values (i.e. a(n) does not go to zero) then the series will diverge because the addition of terms will not stop!