HELP Can anyone PLEASE give me a hand with this limit? THANKS ;)

CathyC
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1. Use the sandwich theorem to compute the limit as n goes to infinity of the sequence with the following nth elements:

a(n) = [1 + sin(n*pi/3)cos(n*pi/5) ] / [n^0.5]

I would really appreciate some help with this one guys. If you could please go slow with the answer as my trig is pretty shaky. Thanks for all your help! :)

Cathy
 
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You don't really have to use a lot of trig. -1<=sin(x)<=1 and the same for cos(x). No matter what x is. Suggest an upper bound for the value of the numerator.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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