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

Sn = 4 + 6 + 8 + ... + 2(n + 1)
Sn = (n/2)(a + Un)
Sn = (n/2)(4 + 2(n + 1))
Sn = (n/2)(n + 6)
Sn = n² + 3n

4(0,2) + 4(0,2)² + 4(0,2)³ + ...
S~ = a/(1 - r)
S~ = 4(0,2)/(1 - 0,2)
S~ = 0,8/0,8
S~ = 1

[4 + 6 + 8 + ... + 2(n + 1)] / (2n - 3) = 5 + 4(0,2) + 4(0,2)² + ...
(n² + 3n) / (2n - 3) = 5 + 1
n² + 3n = 6(2n - 3)
n² + 3n = 12n - 18
n² - 9n + 18 = 0
(n - 3)(n - 6) = 0
n = 3 atau n = 6