Question

Nilai p=1/3+1/9+1/27+1/81+⋯

Answer 1

P = 1/3 + 1/9 + 1/27 + 1/81 + ...
P = 1/3 ( 1 + 1/3 + 1/9 + 1/27 + 1/81 + ...)
P = 1/3 ( 1 + (1/3 + 1/9 + 1/27 + 1/81 +...))
P = 1/3 ( 1 + P)
3P = 1 + P
2P = 1
  P = 1/2

Answer 2

Deret geo tak hingga
a = 1/3
r = (1/9) / (1/3)
= 1/3

S~ = a/(1 - r)
= (1/3) / (1 - 1/3)
= (1/3) / (2/3)
= 1/2