Calculate the limitlimn→∞(2n)!
1/n2.

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

Prove thatlimn→∞n2 · 2nn! = 0

Prove that the sequence (xn)n≥1 converges and compute limn→∞ xn

Prove thatlimn→∞(4n)1/n = 1

Calculate the following quantities:(a) lim infn→∞ (−1)n3 + 1n