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\(P=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+....+\frac{1}{2016}.\left(1+2+3+...+2016\right)\)
\(P=1+\frac{1}{2}.3+\frac{1}{3}.6+\frac{1}{4}.10+....+\frac{1}{2016}.2033136\)
\(P=1+\frac{3}{2}+4+\frac{5}{2}+....+\frac{2017}{2}\)
\(P=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+....+\frac{2017}{2}\)
\(P=\frac{2+3+4+5+....+2017}{2}=\frac{2035152}{2}=1017576\)
\(\frac{-1}{2}\cdot17,5-\frac{2015}{2016}\cdot2018+\frac{1}{2}\cdot7,5+\frac{2015}{2016}\cdot2\)
\(=-\frac{1}{2}\left(17,5-7,5\right)-\frac{2015}{2016}\left(2018-2\right)\)
\(=-\frac{1}{2}\cdot10-\frac{2015}{2016}\cdot2016=-5-2015=-2020\)
Đặt A= 1+2+22+23+...+22015
<=> 2A=2+22+23+...+22016
2A-A=(2+22+23+...+22016)-(1+2+22+...+22015)
<=> A=22016-1
B =\(\frac{1+2+2^2+2^3+...+2^{2015}}{1-2^{2016}}\)
=\(\frac{2^{2016}-1}{1-2^{2016}}\)
=\(\frac{-\left(1-2^{2016}\right)}{1-2^{2016}}\)
=-1
Vậy B=-1
\(A=\left(\frac{1}{2016}+1\right)+\left(\frac{2}{2015}+1\right)+...+\left(\frac{2015}{2}+1\right)+1\)
= \(\frac{2017}{2016}+\frac{2017}{2015}+\frac{2017}{2014}+...\frac{2017}{2}+\frac{2017}{2017}\)
= \(2017\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{2017\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}}\)
= 2017
Chúc bạn học giỏi!
A= -8/5: (1+2/3)
= -8/5:5/3
= -8/5.3/5
= -24/25
B= 7/5.15/49-22/15: 11/5
= 3/7-2/5
= 1/35
\(A=-1,6:\left(1+\frac{2}{3}\right)\)
\(A=-1,6:\frac{5}{3}\)
\(A=-\frac{24}{25}\)
\(B=1,4.\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):2\frac{1}{5}\)
\(B=\frac{135}{98}-\frac{2}{3}\)
\(B=\frac{209}{294}\)
Bài 1: Tính giá trị các biểu thức:
1) \(A=\frac{2}{3}.\frac{2014}{2013}-\frac{2}{3}.\frac{1}{2013}+\frac{1}{3}\)
\(=\frac{2}{3}.\left(\frac{2014}{2013}-\frac{1}{2013}\right)+\frac{1}{3}\)
\(=\frac{2}{3}.1+\frac{1}{3}\)
= 1
Đặt tử là A, ta có:
2A=2(1+2+22+...+22015)
2A=2+22+...+22016
2A-A=(2+22+...+22016)-(1+2+22+...+22015)
A=22016-1
Thay A vào tử của B ta được:\(B=\frac{2^{2016}-1}{1-2^{2016}}=-1\)
Đặt :
Sáng = 1+2+22+23+...+22015
2.Sáng = 21+22+23+...+22016
=> 2. Sáng - Sáng = Sáng = (21+22+23+...+22016) - ( 1+21+22+23+...+22015)
= 22016-1
Thay Sáng vào tử số ta đc :
\(\frac{2^{2016}-1}{1-2^{2016}}\)
Xong