Question

B1:

a. (2⁸.4.13+2⁷.8.65):(2⁹.39)

b. tính tổng 4+2²+2³+2⁴+...+2²⁰

B2:

tìm số tự nhiên x biết:

\(\frac{1.2+2.3+3.4+...+99.100}{x^2+\left(x^2+1\right)+\left(x^2+2\right)+...+\left(x^2+99\right)}=50\frac{116}{131}\)

Answer 1

Bài 1:

a) Ta có: \(\frac{2^8\cdot4\cdot13+2^7\cdot8\cdot65}{2^9\cdot39}\)

\(=\frac{2^8\cdot4\cdot13+2^8\cdot4\cdot13\cdot5}{2^9\cdot39}\)

\(=\frac{2^{10}\cdot13\left(1+5\right)}{2^9\cdot13\cdot3}=\frac{6}{3}=2\)

b) Đặt \(A=4+2^2+2^3+2^4+...+2^{20}\)

Ta có: \(A=4+2^2+2^3+2^4+...+2^{20}\)

\(\Rightarrow2A=2^3+2^3+2^4+...+2^{21}\)

Ta có: \(2A-A=2^3+2^{21}-2^2-2^2=8+2^{21}-8=2^{21}\)

hay \(A=2^{21}\)

Vậy: \(4+2^2+2^3+2^4+...+2^{20}=2^{21}\)