Proving Convergence of Sequence an: limn→∞an

[e.gedge]

Let a_n= ( 2n ) 4^-n, for all n greater than or equal to 1
( n )

Prove that sequence a_n converges to a limit, and find lim_n->infinitya_n.

 

[e.gedge]

that was supposed to be

( 2n )
( n )

 

[e.gedge]

As in, 2n choose n

 

[HallsofIvy]

_{2n}C_n is a polynomial in n and 4^-n, being exponential, goes to 0 faster than any polynomial goes to infinity.