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NN
15 tháng 11 2017
1) \(A=1+2+2^2+2^3+......+2^{2015}\)
\(\Leftrightarrow2A=2+2^2+2^3+......+2^{2016}\)
\(\Leftrightarrow2A-A=\left(2+2^2+2^3+......+2^{2016}\right)-\left(1+2+2^2+2^3+......+2^{2015}\right)\)
\(\Leftrightarrow A=2^{2016}-1\)
Vậy \(A=2^{2016}-1\)
6)Ta có: \(13+23+33+43+.......+103=3025\)
\(\Leftrightarrow2.13+2.23+2.33+2.43+.......+2.103=2.3025\)
\(\Leftrightarrow26+46+66+86+.......+206=6050\)
\(\Leftrightarrow\left(23+3\right)+\left(43+3\right)+\left(63+3\right)+\left(83+3\right)+.......+\left(203+3\right)=6050\)
\(\Leftrightarrow23+43+63+83+.......+203+3.10=6050\)
\(\Leftrightarrow23+43+63+83+.......+203+=6050-30\)
\(\Leftrightarrow23+43+63+83+.......+203+=6020\)
Vậy S=6020
15 tháng 11 2017
b, B có 19 thừa số
=> \(-B=(1-\frac{1}{4})(1-\frac{1}{9})(1-\frac{1}{16})...(1-\frac{1}{400}) \)
<=>\(-B=\frac{(2-1)(2+1)(3-1)(3+1)(4-1)(4+1)...(20-1)(20+1)}{4.9.16...400} \)
<=>\(-B=\frac{(1.2.3.4...19)(3.4.5...21)}{(2.3.4.5.6...20)(2.3.4.5...20)} \)
<=>\(-B=\frac{21}{20.2} =\frac{21}{40} \)
<=>\(B=\frac{-21}{40} \)
29 tháng 8 2022
\(N=4\cdot16\cdot\dfrac{9}{16}\cdot\dfrac{4}{5}\cdot\dfrac{27}{8}=4\cdot9\cdot\dfrac{4}{5}\cdot\dfrac{27}{8}\)
\(=\dfrac{16}{5}\cdot\dfrac{243}{8}=\dfrac{486}{5}\)
HN
18 tháng 4 2017
\(\cos\dfrac{\pi}{15}.\cos\dfrac{2\pi}{15}...\cos\dfrac{7\pi}{15}=-\dfrac{1}{2}.\left(\cos\dfrac{\pi}{15}.\cos\dfrac{2\pi}{15}.\cos\dfrac{4\pi}{15}.\cos\dfrac{8\pi}{15}\right).\left(\cos\dfrac{3\pi}{15}.\cos\dfrac{6\pi}{15}\right)\)
\(=-\dfrac{1}{2}.\left(\cos\dfrac{\pi}{15}.\cos\left(2.\dfrac{\pi}{15}\right).\cos\left(2^2.\dfrac{\pi}{15}\right).\cos\left(2^3\dfrac{\pi}{15}\right)\right).\left(\cos\dfrac{3\pi}{15}.\cos\left(2.\dfrac{3\pi}{15}\right)\right)\)
\(=-\dfrac{1}{2}.\left(\dfrac{\sin\left(2^4.\dfrac{\pi}{15}\right)}{16.\sin\left(\dfrac{\pi}{15}\right)}\right).\left(\dfrac{\sin\left(2^2\dfrac{3\pi}{15}\right)}{4.\sin\left(\dfrac{3\pi}{15}\right)}\right)\)
\(=-\dfrac{1}{2}.\left(\dfrac{\sin\left(\dfrac{16\pi}{15}\right)}{16.\sin\left(\dfrac{\pi}{15}\right)}\right).\left(\dfrac{\sin\left(\dfrac{12\pi}{15}\right)}{4.\sin\left(\dfrac{3\pi}{15}\right)}\right)\)
\(=-\dfrac{1}{2}.\left(\dfrac{-\sin\left(\dfrac{\pi}{15}\right)}{16.\sin\left(\dfrac{\pi}{15}\right)}\right).\left(\dfrac{\sin\left(\dfrac{3\pi}{15}\right)}{4.\sin\left(\dfrac{3\pi}{15}\right)}\right)=\dfrac{1}{128}\)
HT
8 tháng 5 2017
\(A=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}{\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\)
\(\Rightarrow A=\dfrac{1}{1-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\) ( Lượt \(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\) ở tử và mẫu )
\(\Rightarrow A=\dfrac{1}{1-\dfrac{1}{24}}\)
\(\Rightarrow A=\dfrac{1}{\dfrac{23}{24}}=\dfrac{24}{23}\)
Vậy \(A=\dfrac{24}{23}\)
18 tháng 7 2018
áp dụng cô si ta có :
\(\dfrac{1}{2a+b}+\dfrac{1}{2b+c}+\dfrac{1}{2c+a}\ge\dfrac{\left(1+1+1\right)^2}{2a+b+2b+c+2c+a}\)
\(=\dfrac{9}{3\left(a+b+c\right)}=\dfrac{3}{a+b+c}\)
HG
0
NV
Nguyễn Việt Lâm
Giáo viên
8 tháng 2 2021
Câu 1 đề sai, chắc chắn 1 trong 2 cái \(cot^2x\) phải có 1 cái là \(cos^2x\)
2.
\(\dfrac{1-sinx}{cosx}-\dfrac{cosx}{1+sinx}=\dfrac{\left(1-sinx\right)\left(1+sinx\right)-cos^2x}{cosx\left(1+sinx\right)}=\dfrac{1-sin^2x-cos^2x}{cosx\left(1+sinx\right)}\)
\(=\dfrac{1-\left(sin^2x+cos^2x\right)}{cosx\left(1+sinx\right)}=\dfrac{1-1}{cosx\left(1+sinx\right)}=0\)
3.
\(\dfrac{tanx}{sinx}-\dfrac{sinx}{cotx}=\dfrac{tanx.cotx-sin^2x}{sinx.cotx}=\dfrac{1-sin^2x}{sinx.\dfrac{cosx}{sinx}}=\dfrac{cos^2x}{cosx}=cosx\)
4.
\(\dfrac{tanx}{1-tan^2x}.\dfrac{cot^2x-1}{cotx}=\dfrac{tanx}{1-tan^2x}.\dfrac{\dfrac{1}{tan^2x}-1}{\dfrac{1}{tanx}}=\dfrac{tanx}{1-tan^2x}.\dfrac{1-tan^2x}{tanx}=1\)
5.
\(\dfrac{1+sin^2x}{1-sin^2x}=\dfrac{1+sin^2x}{cos^2x}=\dfrac{1}{cos^2x}+tan^2x=\dfrac{sin^2x+cos^2x}{cos^2x}+tan^2x\)
\(=tan^2x+1+tan^2x=1+2tan^2x\)
H
1
BU
1 tháng 4 2022
\(\cos a\times\sin b=-\dfrac{1}{2}\left[\sin\left(a-b\right)-\sin\left(a+b\right)\right]\)
\(=-\dfrac{1}{2}\left(\dfrac{1}{3}+\dfrac{2}{3}\right)=\dfrac{-1}{2}\times1=-\dfrac{1}{2}\)
A=\(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\)=\(\dfrac{5}{3}\)=0.625
0.625 > 8998
like cho mình nha!