Câu hỏi của Nguyễn Ngọc Gia Hân

Question

Thu gọn tổng sau :

1 - 2 + 2² - 2³ + 2⁴ - .... + 2¹⁰⁰⁰

Bùi Ngọc Minh · Accepted Answer

Đặt A=$1-2+2^2-2^3+2^4-...+2^{1000}$

A.2=$2.\left(1-2+2^2-2^3+2^4-...+2^{1000}\right)$

A.2=$2-2^2+2^3-2^4+...+2^{1001}$

A.2+A=$\left(2-2^2+2^3-2^4+...+2^{1001}\right)+\left(1-2+2^2-2^3+...+2^{1000}\right)$

A.3=$2^{1001}+1$

A=$\dfrac{2^{1001}+1}{3}$

Câu trả lời:

Đặt A=$1-2+2^2-2^3+2^4-...+2^{1000}$

A.2=$2.\left(1-2+2^2-2^3+2^4-...+2^{1000}\right)$

A.2=$2-2^2+2^3-2^4+...+2^{1001}$

A.2+A=$\left(2-2^2+2^3-2^4+...+2^{1001}\right)+\left(1-2+2^2-2^3+...+2^{1000}\right)$

A.3=$2^{1001}+1$

A=$\dfrac{2^{1001}+1}{3}$