Calculate the limit of the series

[sedaw]

need to calculate the limit of the series

(cos(a/n))^(n^3) n goes to infinity and a=!0


i try that :

e^L


L= the limit of (n^3)*ln(cos(a/n))


what now ?


TNX !

 

[Dick]

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.

 

[sedaw]

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.

hello Dick !

first of all tnx.

i can't use l'Hopital's theorem cause n =1,2,3...

so F(n) not differentiable .

 

[Dick]

f(x)=ln(cos(a/x))*x^3 is differentiable. If you know the limit of f(x) as x->infinity, then you know the limit of L as n->infinity.