Question

[Pham Trong Bach]

Tính tổng  $S=1+2.2+{3.2}^2+{4.2}^3+\mathrm{...}+{2018.2}^{2017}.$

A.  $S={2017.2}^{2018}+1.$

B.  $S={2017.2}^{2018}.$

C.  $S={2018.2}^{2018}+1.$

D.  $S={2019.2}^{2018}+1.$

Answer 1

[Cao Minh Tâm]

Đáp án A

y = x + x 2 + x 3 + ... + x 2018 = x 1 − x 2018 1 − x y ' = 1 + 2 x + 3 x 2 + ... + 2018 x 2017         = 2018 x 2019 − 2019 x 2018 + 1 ( 1 − x ) 2 y ' ( 2 ) = 1 + 2.2 + 3.2 2 + ... + 2018.2 2017 = 2017.2 2018 + 1