> a:=factorial(n)/2^(n^2); factorial(n) a := ------------ / 2\ \n / 2 > limit(a,n=infinity); 0 > b:=n^n/(4^n*factorial(n)); n n b := --------------- n 4 factorial(n) > limit(b,n=infinity); 0 > S:=sum(k,k=1..n); 1 2 1 1 S := - (n + 1) - - n - - 2 2 2 > expand(S); 1 2 1 - n + - n 2 2 > S:=sum(k^2,k=1..n); 1 3 1 2 1 1 S := - (n + 1) - - (n + 1) + - n + - 3 2 6 6 > expand(S); 1 3 1 2 1 - n + - n + - n 3 2 6 > f:=x^2-2; 2 f := x - 2 > g:=-x^2+3; 2 g := -x + 3 > plot({f,g},x=-2..2); > sols:=solve(f=g,x); 1 (1/2) 1 (1/2) sols := - 10 , - - 10 2 2 > a:=sols[1]; 1 (1/2) a := - 10 2 > b:=sols[2]; 1 (1/2) b := - - 10 2 > area:=int(f-g,x=a..b); 10 (1/2) area := -- 10 3 > taylor(exp(x),x=0,3); 1 2 / 3\ 1 + x + - x + O\x / 2 > T:=taylor((exp(x)-1)/x,x=0,4); 1 1 2 / 3\ T := 1 + - x + - x + O\x / 2 6 > P:=convert(T,polynom); 1 1 2 P := 1 + - x + - x 2 6 > G:=int(P,x); 1 2 1 3 G := x + - x + -- x 4 18 > subs(x=1,G)-subs(x=0,G); 47 -- 36 >