dari suatu deret geometri konvergen diketahui u1-u3 =8 dan 3log u1 + 3log u2 + 3log u3 = 3 tentukan jumlah tak hingga

³log a + ³log ar + ³log ar² = 3
³log (a x ar x ar²) = ³log 3³
a³r³ = 3³
ar = 3....a = 3/r

u1-u3 = 8
a - ar² = 8
3/r - (3/r)r² = 8
3/r - 3r = 8
3r + 8 - 3/r = 0
kalikan dgn r
3r² + 8r - 3 = 0
(3r - 1)(r + 3)= 0
3r = 1 ... r=1/3
r = -3 (bukan konvergen)

r=1/3 .... a=3/(1/3)= 3 x 3/1 = 9

deret tak hingga S
S = a/(1-r)
=9 / (1-1/3)
=9 / (2/3)
=9 x 3/2
= 27/2