Aufgabe 13

Limit[(1/(n^3)) Sum[(k^2), {k, 1, n}], n -> Infinity]

Aufgabe 14

liste = Table[Sum[(1/(k!)), {k, 0, n}], {n, 1, 10}]

liste // N

N[liste, 20]

Aufgabe 15

a[0] = 1; 
    a[n_] := a[n] = (1/2) (a[n - 1] + (3/a)[n - 1])

N[Table[a[n], {n, 1, 10}], 20]

Aufgabe 16

Limit[(Sqrt[(n^2) - 2  n]) - (Sqrt[(n^2) - 3  n]), 
      n -> ∞]

Aufgabe 17

a = {1, 2, 3}; b = {4, 5, 6}; c = {7, 8, λ};

Cross[a, b] . c

Solve[Cross[a, b] . c == 0, λ]

Aufgabe 18

Clear[s]

sol = 
      Solve[{4, 2, -1} + t*{12, 6, -24} == {7, 3, 2} + 
            s*{3, -2, 1}, {t, s}]

sol = 
      Solve[{5, 4, 6} + t*{2, 4, 6} == {-2, -2, 1} + 
            s*{3, 2, 1}, {t, s}]

{5, 4, 6} + t*{2, 4, 6} /. sol[[1]]