Question

Tentukan nilai n yang memenuhi

(4+6+....+2(n+1)) / (2n-3) = 5 + 4(0,2) +4(0,2)^2 + ....

Answer 1

Verified answer

...
deret

misal p = 4 + 6+ ...+ 2(n+1)
p = 4 + 6 + ...+ (2n +2)  ---> deret aritmetika
p = sn = n/2 ( a + un)
p = n/2(4 + 2n+ 2)
p = n/2 ( 2n + 6)
p = n ( n + 3)

q = 4 (0,2) + 4(0,2)^2 + ... --> deret geometri
q = 0,8 + 0,16 +...
a = 0,8
r = 0,2
q = s~ =  a/(1 - r) = 0,8 / (1 - 0,2) = 0,8 /(0.8) = 1

(4 + 6 + 2(n+1) / (2n -3) = 5 + 4 (0,2) + 4(0,2)^2 + ..
(p) / (2n -3)  = 5 + q
n (n+3) / (2n-3) = 5 + 1
n²  + 3n = 6(2n -3)
n²  + 3n =  12n - 18
n² - 9n + 18 = 0
(n - 6)(n - 3) =0
n = 6 atau n = 3