Seems AsymptoticSum still can't solve many really simple sums though, like AsymptoticSum[Binomial[n,k],{k,0,n/3},{n,Infinity,1}] Will still have to that b

Seems AsymptoticSum still can't solve many really simple sums though, like AsymptoticSum[Binomial[n,k],{k,0,n/3},{n,Infinity,1}] Will still have to that by hand I guess :(