f = Product[((2^i)/(16(i^2))),{i,2,n-1}];
g = ((2^(n^2))/(n!));

Limit[(f/g), n->Infinity]

fun = {7^(10n),n^9,n^8, ((2^(n^2))/(n!))};
Table[Limit[f/i, n->Infinity],{i, fun}]

fun = {7^(10n),n^9,n^8, ((2^(n^2))/(n!))};
Table[i->Limit[f/i, n->Infinity],{i, fun}]

fun = {(n^5),(n^3),(n^2),(n^4),(n^6)};
Table[Limit[Sum[Sum[1,{j,1,i+6}],{i,1,(n^3)+2}]/i, n->Infinity],{i, fun}]

<<Vilcretas`

?CompLimit

CompLimit[{((15(n^4)+17(n^3)+20(n^2)-4n+16)/(6(n^4)+13(n^3)+19(n^2)+17n+16)),((15(n^j)+10(n^2)+3n+19)/(8(n^4)-14(n^3)+19(n^2)-9n+11))}, jvalor->100]

Programa1[n_,valor_:60/5846006549323611671624303190352640062064535163787]:=If[n==6,valor,Programa1[n-1,valor*((3+19*(-3+n))/(-8^(18*(-3+n))+13^(9*(-3+n))-20^(7*(-3+n))))]]

Programa2[n_]:=If[n==6,60/5846006549323611671624303190352640062064535163787,Programa2[n-1]*((3+19*(-3+n))/(-8^(18*(-3+n))+13^(9*(-3+n))-20^(7*(-3+n))))]

Programa3[n_]:=Module[{i,valor=1},For[i=3,i<=n-3,valor=valor*(3+19*i)/(8^(18*i)-13^(9*i)+20^(7*i));
i++];
valor]

Programa4[n_]:=Product[(3+19*i)/(8^(18*i)-13^(9*i)+20^(7*i)),{i,3,n-3}]

Table[Programa1[i]==Programa2[i]==Programa3[i]==Programa4[i], {i,3,10}]

?PruebaADAGrafica

PruebaADAGrafica[{Programa1,Programa2, Programa3, Programa4}, 25,6]

PruebaADAGrafica[{Programa1,Programa2, Programa3, Programa4}, 25,6]

programa1[n_,valor_:78124999/175781250]:=If[n==1,valor,programa1[n-1,valor+((5^(-10 n))*(-1+2*5^(10 n)+6*5^(10 n)*n^3))/(2*(2+7*n^2))]]

programa2[n_]:=If[n==1,78124999/175781250,programa2[n-1]+((5^(-10 n))*(-1+2*5^(10 n)+6*5^(10 n)*n^3))/(2*(2+7*n^2))]

?PruebaADA2

PruebaADA2[{programa1, programa2}, 200,1,20]

PruebaADA2[{programa1, programa2}, 200,1,20]

PruebaADA2[{programa1, programa2}, 200,1,20]

PruebaADA2[{programa1, programa2}, 200,1,20]

PruebaADA2[{programa1, programa2}, 200,1,20]

PruebaADAGrafica[{programa1, programa2}, 200, 1, 20]