Câu hỏi của Lori Sen

Question

Bài 1 : Tính tổng :

a) A = 1 + 2 + 2² + 2³ + 2⁴ + ..... + 2³⁰

b) B = 3² + 3³ + 3⁴ + ..... + 3⁵⁰<...

Đức Phạm · Accepted Answer

$A=1+2+2^2+2^3+2^4+....+2^{30}$

$2A=2+2^2+2^3+2^4+....++2^{30}+2^{31}$

$2A-A=\left(2+2^2+2^3+2^4+....+2^{30}+2^{31}\right)-\left(2+2^2+2^3+2^4+....+2^{30}\right)$

$\Rightarrow A=2^{31}-1$

Câu trả lời:

$A=1+2+2^2+2^3+2^4+....+2^{30}$

$2A=2+2^2+2^3+2^4+....++2^{30}+2^{31}$

$2A-A=\left(2+2^2+2^3+2^4+....+2^{30}+2^{31}\right)-\left(2+2^2+2^3+2^4+....+2^{30}\right)$

$\Rightarrow A=2^{31}-1$