dowodzenie ***KIEŁBASA***: 27D wykaż że jeśli: a₁ a₂ a_n − = − = = − b₁ b₂ ... b_n i b₁+b₂+...+b_n≠0 to a₁+a₂+...+a_n a₁ −−−−−−−−−− = − b₁+b₂+...+b_n b₁

Bogdan:

a1		a2		an
	=		= ... =
b1		b2		bn

a1		a2		k1*a1		an		kn−1*a1
	,		=		, .. ,		=
b1		b2		k1*b1		bn		kn−1*b1

a1 + a2 + ... + an
	=
b1 + b2 + ... + bn

	a1 + k1*a1 + ... + k*n−1*a1
=		=
	b1 + k1*b1 + ... + k*n−1*b1

	a1(1 + k1 + ... + kn−1)		a1
=		=
	b1(1 + k1 + ... + kn−1)		b1

AS: Niech an/bn = k dla n = 1,2,3,... Wówczas a1/b1 = k ⇒ a1 = k*b1 a2/b2 = k ⇒ a2 = k*b2 itd a1 + a2 + ... + an k*b1 + k*b2 +..+.k*bn k*(b1 + b2 +... + bn) a1 −−−−−−−−−−−−− = −−−−−−−−−−−−−− = −−−−−−−−−−−−−−−− = k = −−− b1 + b2 + ... + bn b1 + b2 + ... + bn b1 + b2 + ... + bn b1 c.n.d.