Załącznik 1 Wzory: [latex]a_n=a_1q^{n-1}[/latex] [latex]S_n= frac{a_1(q^n-1)}{q-1}[/latex] --------------------------------------- [latex]a_1=?[/latex] [latex]q= frac{1}{2}[/latex] [latex]n=10[/latex] [latex]S_{10}=4-frac{1}{2^8}[/latex] [latex]4-frac{1}{2^8}= frac{a_1(( frac{1}{2} )^{10}-1)}{ frac{1}{2} -1}[/latex] [latex]2^2-frac{1}{2^8}=frac{a_1(frac{1}{2^{10}}-1)}{- frac{1}{2} }[/latex] [latex]frac{2^{10}-1}{2^8}=-frac{a_1(frac{1-2^{10}}{2^{10}})}{frac{1}{2} }[/latex] [latex]frac{2^{10}-1}{2^8}=frac{a_1(frac{2^{10}-1}{2^{10}})}{2^{-1}}[/latex] [latex]frac{2^{10}-1}{2^8}=frac{a_1(2^{10}-1)}{2^{-1}cdot 2^{10}}[/latex] [latex]frac{2^{10}-1}{2^8}=frac{a_1(2^{10}-1)}{2^{9}} /cdot frac{2^8}{2^{10}-1}[/latex] [latex]1= frac{a_1}{2}[/latex] [latex]a_1=2[/latex] --------------------------------------- [latex]a_1=-5[/latex] [latex]q=0,1[/latex] [latex]n=4[/latex] [latex]S_{4}=?[/latex] [latex]S_4= frac{-5cdot (0,1^4-1)}{0,1-1}[/latex] [latex]S_4= frac{-5cdot (0,0001-1)}{-0,9}[/latex] [latex]S_4=-5cdot 1,111[/latex] [latex]S_4=-5,555[/latex] --------------------------------------- [latex]a_1=3[/latex] [latex]q=?[/latex] [latex]n=2[/latex] [latex]S_{2}=5[/latex] [latex]5= frac{3(q^2-1)}{q-1}[/latex] [latex]5= frac{3(q-1)(q+1)}{q-1}[/latex] [latex]5=3(q+1)[/latex] [latex]5=3q+3[/latex] [latex]-3q=3-5[/latex] [latex]-3q=-2 /:(-3)[/latex] [latex]q=frac{2}{3}[/latex] ================================= Załącznik 2 [latex]frac{3x-1}{x^2+2x}[/latex] ----------------------- [latex]x=-3[/latex] [latex]frac{3x-1}{x^2+2x}=frac{3cdot (-3)-1}{(-3)^2+2cdot (-3)}=[/latex] [latex]frac{-9-1}{9-6}= frac{-10}{3}=-3 frac{1}{3}[/latex] ----------------------- [latex]x=4[/latex] [latex]frac{3x-1}{x^2+2x}=frac{3cdot 4-1}{4^2+2cdot 4}=[/latex] [latex]frac{12-1}{16+8}= frac{11}{24}[/latex] ----------------------- [latex]x=9[/latex] [latex]frac{3x-1}{x^2+2x}=frac{3cdot 9-1}{9^2+2cdot 9}=[/latex] [latex]frac{27-1}{81+18}= frac{26}{99}[/latex] ================================= Załącznik 3 [latex]frac{4y-xy}{x+2y}[/latex] ----------------------- [latex]x=-1,y=5[/latex] [latex]frac{4y-xy}{x+2y}=frac{4cdot 5-(-1)cdot 5}{-1+2cdot 5}=[/latex] [latex]frac{20+5}{-1+10}= frac{25}{9}=2 frac{7}{9}[/latex] ----------------------- [latex]x=3,y=5[/latex] [latex]frac{4y-xy}{x+2y}= frac{4cdot 5-3cdot 5}{3+2cdot 5}=[/latex] [latex]frac{20-15}{3+10}= frac{5}{13}[/latex]
zad1.Uzupelnij brakujace wielkosci w tabeli obok wiedzac ze ciag (an) jest ciagiem geometrycznym o ilorazie q tabelka w zalaczniku daje najj zad2.Dla podanych wartosci zmniennych oblicz wartosc wyrazenia w zalaczniku ...
