Question

Untuk harga harga x manakah deret geometri tak hingga berikut ini konvergen, jikaa rasionya sama dengan:
a. X-2
b. log ( x - 2 )
c. ³log ( x - 1 )

Answer 1

Verified answer

Deret geometri tak hingga akan konvergen jika
-1 < r < 1

a) r = x - 2
-1 < x - 2 < 1
-1 + 2 < x - 2 + 2 < 1 + 2
1 < x < 3

b) r = log (x - 2)
-1 < log (x - 2) < 1
log 10^-2 < log (x - 2) < log 10
1/10 < x - 2 < 10
1/10 + 2 < x - 2 + 2 < 10 + 2
21/10 < x < 12

c) r = ³log (x - 1)
-1 < ³log (x - 1) < 1
³log 3^-1 < ³log (x - 1) < ³log 3
1/3 < x - 1 < 3
1/3 + 1 < x - 1 + 1 < 3 + 1
4/3 < x < 4