Nilai dari 1 + 2.2 + 3.2² + 4.2³ + ... + 2018.2²⁰¹⁷ adalah...

1 + 2.2 + 3.2^2 + 4.2^3 + ... + 2018.2^(2017) = (n).2^(n - 1) [n = 1 .. 2018]

= (n).(2^n)/2


= n.2^n + 2^n [n = 0 .. 2017]

Untuk n.2^n
1.2^1 = 2 = 2 + 0.2^2
1.2^1 + 2.2^2 = 2 + 8 = 2 + 1.2^3
1.2^1 + 2.2^2 + 3.2^3 = 2 + 8 + 24 = 2 + 32 = 2 + 2.2^4
dst.
maka,
Sum n.2^n = 2 + (n - 1).2^(n + 1)

Maka,
(n).(2^n)/2 [n = 1 .. 2018] = (2 + (2018 - 1).2^(2018 + 1))/2
= 1 + 2017.2^(2018 + 1 - 1)
= 1 + 2017.2^(2018)

B.