Question

[nguyễn tường nhi]

2+2^2+2^3+...+2^100-2^101

Answer 1

[Hồ Đức Việt]

Chữa đề: Ta thu gọn A

A=2+2^2+2^3+...+2^100-2^101

2A=2^2+2^3+2^4+...+2^101-2^102

2A-A=2^101-2-2^102

Vậy A= 2^101-2-2^102

Answer 2

[༺༒༻²ᵏ⁸]

\(\text{Đ}\text{ặt}B=2+2^2+2^3+...+2^{100}-2^{101}\)

\(\text{Đ}\text{ặt}A=2+2^2+...+2^{100}\)

\(2A=2^2+2^3+2^4+...+2^{101}-2^{102}\)

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

\(A=2^2+2^3+2^4+...+2^{101}-2-2^2-2^3-...-2^{100}\)

\(A=2^{101}-2\)

Thay A vào B ta được:

\(B=2^{101}-2-2^{101}\)

\(B=2^{101}-2^{101}-2\)

\(B=0-2\)

\(B=\left(-2\right)\)