a) a1 = 3 oraz q = -2 S₅ = 3*[1 -(-2)⁵]/[1 - (-2)] = 3*[1 +32]/3 = 33 b) bn = 5/(2n) b1 = 5/2 b2 = 5/4 b3 = 5/8 q = b3 :b2 = b2 : b1 = 1/2 S₇ = (5/2)*[1 - (1/2)⁷]/[1 - 1/2] = (5/2)*[1 - 1/128]/(1/2) = = 5*(127/128) = 635/128 c) Tutaj jest zapewne pomyłka Winno być: 22, -66, 198 a1 = 22 q =-66 : 22 = 198 :(-66) = - 3 S₆ = 22*[1 - (-3)⁶]/[1 - (-3)] = 22*[1 - 729]/4 = 22*(-728)/4 = - 4 004 ========================================================
a) a1 =3, q =(-2) Sn =a1 x (1-q^n)/(1-q) S5 = 3 x [1-(-2)^5]/[1-(-2)] =3 x(1+32)/(1+2) =3 x 33/3 =33 b) Bn =5/2n b1 =5/2 b2 =5/4 b3 =5/8 q =b3/b2 = b2/b1 q = 5/8:5/4 = 5/4:5/2 =1/2 S7 =b1 x (1-q^7)/(1-q) =5/2 x [1 -(1/2)^7/(1-1/2) =5/2 x (127/128:1/2) S7 = 635//128 c) 22, -66, 198 a1 =22 q = -66/22 =198/-66 = -3 S6 =a1 x (1-q^6)/(1-q) = 22 x [1-(-3)^6]/(1+3) =22 x (1-729)/4 S6 =22 x(- 728)/4 = -4004
