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(1/2+2015/2016+1 )nhaân (2016/2017+7/2) - (1/2+2015/2016) nhaân (7/2+2016/2017 +1)
TÍNH PHEP TÍNH NAY


\(\frac{B}{A}=\frac{\frac{2016}{1}+\frac{2015}{2}+...+\frac{2}{2015}+\frac{1}{2016}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+..+\frac{1}{2016}+\frac{1}{2017}}\)
\(\frac{B}{A}=\frac{\left(\frac{2016}{1}+1\right)+\left(\frac{2015}{2}+1\right)+...+\left(\frac{1}{2016}+1\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}}\)
\(\frac{B}{A}=\frac{\frac{2017}{1}+\frac{2017}{2}+...+\frac{2017}{2016}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}}\)
\(\frac{B}{A}=\frac{2017\cdot\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}}=2017\div\frac{1}{2017}=4068289\)

\(A=2^{2017}-(2^{2016}+2^{2015}+......+2^1+2^0)\)
Đặt \(B=2^{2016}+2^{2015}+.....+2^1+2^0\)
\(\Rightarrow2B=2^{2017}+2^{2016}+....+2^1+2^0\)
\(\Rightarrow2B-B=(2^{2017}+2^{2016}+...+2^0)-(2^{2016}+2^{2015}+...+2^1+2^0)\)
\(\Rightarrow B=2^{2017}-2^0\)
\(\Rightarrow A=2^{2017}-(2^{2017}-1)\)
\(\Rightarrow A=1\)
2A = 22018 - (22017 + 22016 + ....+ 21)
2A - A = [22018 - (22017 + 22016 + ....+ 21 )] - [22017 - (22016 + 22015 +..... + 21 + 20)
A = 22018 - 22017 - 22017 - 1
A = 22018 - (22017 +22017 +1)
A = 22018 - (22018 +1 )
A = -1

Theo mình bạn không nên hỏi những bài thế này vì nó rất easy
\(A=2^{2017}-\left(2^{2016}+2^{2015}+...+2^2+2^1+2^0\right)\)
\(A=2^{2017}-\left(2^0+2^1+2^2+...+2^{2015}+2^{2016}\right)\)
\(B=\left(2^0+2^1+2^2+...+2^{2015}+2^{2016}\right)\)
\(2B=\left(2^1+2^2+2^3+...+2^{2016}+2^{2017}\right)\)
\(B=\left(2^1+2^2+2^3+...+2^{2016}+2^{2017}\right)-\left(2^0+2^2+2^3+...+2^{2016}+2^{2017}\right)\)
\(B=2^{2017}-2^0=2^{2017}-1\)
\(A=2^{2017}-\left(2^{2017}-1\right)=2^{2017}-2^{2017}+1=1\)