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Sandwich Theorem

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1 Answer

Since 0 <= cos(n) <= 1, therefore
 
0/(10n^2) <= cos(n)/(10n^2) <= 1/(10n^2)
 
Now, find the limits to the sequences on the left and right:
 
lim {0/(10n^2)} = lim{0} = 0
 
lim{1 / (10n^2)} = 0
 
Therefore, the sandwich theorem holds that the limit of cos(n)/(10n^2) is also 0.