Prove thatlimn→∞n2 · 2nn! = 0

Calculate the limitlimn→∞(2n)!
1/n2.

Prove thatlimn→∞(4n)1/n = 1

Prove thatlimn→∞Z 10fn = 0.Hint) Use the comparison principle

Evaluate:       2 ! 1 !lim 2 ! 1 !nn nn n   

Prove that the series ∞Xn=12nn!is convergent.1