Question

Hitunglah jumlah 10 suka pertama deret 1/3 + 1/6 +1/12 + .....

Answer 1

Cari deret geometri atau aritmatka ? klo dia geometri banyak n berapa ?
Kalau dia deret geometri berarti ini salah satu deret geometri tak hingga ya ?
a = 1/3 ; r = 1/2
oke langsung saja ke rumus.
S∞ = a / (1 - r ) 
      = 1/3 / ( 1 - 1/2 ) 
      = 2/3

Sn = a ( 1 - r^n )
            1 - r
S10 = 1/3 ( 1 - 1/2^10 ) / ( 1 - 1/2 )
       = 1/3 ( 1 - 1/1024 ) / ( 1/2 )
       = 1/3 ( 1 - 1/1024 ) x 2
       = 341/1024 x 2
       = 341/512

Answer 2

A = 1/3
r = U2/U1 = (1/6)/(1/3) = 1/2

⇒ Jumlah 10 suku pertama:
Sn = (a (1 - r^n)) / (r - 1)
S10 = (1/3 (1 - (1/2)^10)) / (1/2 - 1)
S10 = (1/3 (1 - 1/1024)) / (1/2)
S10 = (1/3 (1023/1024)) / (1/2)
S10 = (1023/3072) / (1/2)
S10 = 1023/3072 * 2
S10 = 2046/3072