Rút gọn biểu thức P= (2-√3)2017 (2+√3)2018
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8 tháng 5 2018
\(A=\frac{\frac{2017}{1}+\frac{2016}{2}+\frac{2015}{3}+...+\frac{1}{2017}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)
\(A=\frac{1+\left(1+\frac{2016}{2}\right)+\left(1+\frac{2015}{3}\right)+...+\left(1+\frac{1}{2017}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)
\(A=\frac{\frac{2018}{2018}+\frac{2018}{2}+\frac{2018}{3}+...+\frac{2018}{2017}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)
\(A=\frac{2018\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}+\frac{1}{2018}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2018}}\)
\(A=2018\)
8 tháng 5 2018
Ta có :
\(A=\frac{\frac{2017}{1}+\frac{2016}{2}+\frac{2015}{3}+...+\frac{1}{2017}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)
\(A=\frac{\left(\frac{2017}{1}-1-1-...-1\right)+\left(\frac{2016}{2}+1\right)+\left(\frac{2015}{3}+1\right)+...+\left(\frac{1}{2017}+1\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)
\(A=\frac{\frac{2018}{2018}+\frac{2018}{2}+\frac{2018}{3}+...+\frac{2018}{2017}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)
\(A=\frac{2018\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}}\)
\(A=2018\)
Vậy \(A=2018\)
Chúc bạn học tốt ~
BM
1
15 tháng 10 2018
\(M=\left(2018^{2019}+2018^{2018}+...+2018^2+2018\right)2017+1\)
Gọi \(A=2018^{2019}+2018^{2018}+...+2018^2+2018\)
\(\Rightarrow2018A=2018^{2020}+2018^{2019}+...+2018^3+2018^2\)
\(\Rightarrow2018A-A=2018^{2020}-2018\)
\(\Rightarrow2017A=2018^{2020}-2018\)
\(\Rightarrow A=\left(2018^{2020}-2018\right)\div2017\)
\(\Rightarrow M=\left(2018^{2020}-2018\right)\div2017.2017+1\)
\(\Rightarrow M=2018^{2020}-2018+1\)
\(\Rightarrow M=2018^{2020}-2017\)
13 tháng 10 2018
Sai đề câu E sửa lại 95 hoặc 93 vì đây là dãy số mũ lẻ. Ta có :
\(E=3+3^3+3^5+3^7+...+3^{95}\)
\(\Rightarrow\) \(9E=3^3+3^5+3^7+3^9+...+3^{95}+3^{97}\)
\(\Rightarrow\) \(8E=3^{97}-3\)
\(\Rightarrow\) \(E=\frac{3^{97}-3}{8}\)
T
13 tháng 10 2018
\(E=3+3^3+3^5+3^7+.......+3^{95}\)
\(\Rightarrow9E=3^3+3^5+3^7+3^9+...+3^{97}\)
\(\Rightarrow9E-E=\left(3^3+3^5+3^7+3^9+....+3^{97}\right)-\left(3+3^3+3^5+3^7+.....+3^{95}\right)\)
\(\Rightarrow8E=3^{97}-3\)
\(\Rightarrow E=\frac{3^{97}-3}{8}\)
\(F=1+2018+2018^2+......+2018^{2017}\)
\(=2018^0+2018^1+2018^2+....+2018^{2017}\)
\(\Rightarrow2018F=2018^1+2018^2+2018^3+....+2018^{2018}\)
\(\Rightarrow2018F-F=\left(2018^1+2018^2+2018^3+....+2018^{2018}\right)-\left(2018^0+2018^1+2018^2+....+2018^{2017}\right)\)
\(\Rightarrow2017F=2018^{2018}-1\)
\(\Rightarrow F=\frac{2018^{2018}-1}{2017}\)
20 tháng 8 2018
Đặt \(D=1^2+2^2+3^2+...+2018^2\)
\(D=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+2018\left(2019-1\right)\)
\(D=1.2-1+2.3-2+3.4-3+...+2018.2019-2018\)
\(D=\left(1.2+2.3+...+2018.2019\right)-\left(1+2+3+...+2018\right)\)
Đặt \(A=1.2+2.3+...+2018.2019\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+2018.2019\left(2020-2017\right)\)
\(\Rightarrow3A=2018.2019.2010\Rightarrow A=\frac{2018.2019.2020}{3}\)
Đặt \(B=1+2+3+...+2018\)
\(B=\frac{\left(2018+1\right)\left(2018-1+1\right)}{2}=\frac{2019.2018}{2}\)
\(\Rightarrow D=A+B=\frac{2018.2019.2020}{3}+\frac{2019.2018}{2}\)
\(\Rightarrow D=\frac{2018.2019.2020.2+2019.2018.3}{6}\)
13 tháng 6 2018
\(A=\left(3m+4n-5p\right)-\left(3m-4n-5p\right)\)
\(\Rightarrow3m+4n-5p-3m+4n+5p=A\)
\(\Rightarrow A=\left(3m-3m\right)+\left(4n+4n\right)-\left(5p-5p\right)\)
\(\Rightarrow A=0+8n+0=8n\)
\(P=\left(2+\sqrt{3}\right)^{-2017}.\left(2+\sqrt{3}\right)^{2018} \)
\(P=\left(2+\sqrt{3}\right)^{-2017+2018}\)
\(P=2+\sqrt{3}\)