Câu hỏi của Nguyễn Vũ Hoàng

Question

(Theo bài toán của cô Ms Hạnh - THCS NX)

Rút gọn tổng sau :

$A=1+2+2^2+2^3+2^4+...+2^{100}$.

Mashiro Shiina · Accepted Answer

$A=1+2+2^2+2^3+2^4+...+2^{100}$

$2A=2+2^2+2^3+2^4+2^5+....+2^{101}$

$2A-A=\left(2+2^2+2^3+2^4+2^5+...+2^{101}\right)-\left(1+2+2^2+2^3+2^4+...+2^{100}\right)$

$A=2^{101}-1$Câu trả lời: $A=1+2+2^2+2^3+2^4+...+2^{100}$

$2A=2+2^2+2^3+2^4+2^5+....+2^{101}$

$2A-A=\left(2+2^2+2^3+2^4+2^5+...+2^{101}\right)-\left(1+2+2^2+2^3+2^4+...+2^{100}\right)$

$A=2^{101}-1$