The limit of the series (cos(a/n))^(n^3) as n approaches infinity, where a ≠ 0, can be calculated using the expression L = (n^3) * ln(cos(a/n)). This limit initially presents a 0*infinity form, necessitating the application of l'Hôpital's theorem. However, since n is a discrete variable (n = 1, 2, 3...), the function must be transformed to f(x) = ln(cos(a/x)) * x^3 for differentiability. The limit of f(x) as x approaches infinity will provide the necessary insight into the limit of L as n approaches infinity.
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Dick said:L has the form 0*infinity. Use l'Hopital's theorem on it to try and figure out the limit. You may have to use l'Hopital more than once.