Tính
A=\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)...\left(1-\frac{1}{2010^2}\right)\)
Làm đầy đủ nha
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\(\Rightarrow\frac{4x^2-4x+1}{3}-\frac{3}{2}\left(x^2+6x+9\right)=\frac{1}{3}\left(x^2-1\right)+2x\)
\(\Rightarrow\frac{4x^2-4x+1}{3}-\frac{3x^2+18x+27}{2}=\frac{x^2-1}{3}+2x\)
\(\Rightarrow8x^2-8x+2-9x^2-54x-81=2x^2-2+12x\)
\(\Rightarrow-3x^2-74x-77=0\)
\(\Delta=5476-4.\left(-77\right).\left(-3\right)=4552\)
\(\Rightarrow\sqrt{\Delta}=\sqrt{4552}\)
\(\Rightarrow x=\frac{-74+\sqrt{4552}}{6};x=\frac{-74-\sqrt{4552}}{6}\)
\(\frac{\left(2x-1\right)^2}{3}-\frac{3.\left(x+3\right)^2}{2}=\frac{x^2-1}{3}+2x\)
Qui đồng lên là tìm được
a) -1 - 2 + 3 + 4 - 5 - 6 + 7 + 8 - 9 - 10 + 11 + 12 - ... - 2013 - 2014 + 2015 + 2016
= ( -1 - 2 + 3 + 4 ) - ( 5 + 6 - 7 - 8 ) - ( 9 + 10 - 11 - 12 ) - .......... - ( 2013 + 2014 - 2015 - 2016 )
= 4 - ( -4 ) - ( -4 ) - ......... - ( -4 )
= 4 + 4 + 4 +....... + 4
= { [ ( 2016 - 1 ) : 1 + 1 ] : 4 } . 4
= { [ 2015 : 1 + 1 ] : 4 } . 4
= { 2016 : 4 } . 4
= 504 . 4
= 2016
b) \(\left(\frac{1}{2}-1\right):\left(\frac{1}{3}-1\right):\left(\frac{1}{4}-1\right):\left(\frac{1}{5}-1\right):.........:\left(\frac{1}{100}-1\right)\)
\(=\frac{-1}{2}:\frac{-2}{3}:\frac{-3}{4}:\frac{-4}{5}:......:\frac{-99}{100}\)
\(=\frac{-1}{2}.\frac{3}{-2}.\frac{4}{-3}.\frac{5}{-4}.......\frac{100}{-99}\)
\(=\frac{-1.3.4........100}{2.2.3.4......99}\)
\(=\frac{-1.100}{2.2}\)
\(=\frac{-100}{4}\)
\(=-25\)
a) -1-2+3+4-5-6+7+8+...+2016=-3+3-7+7-...-2016+2016=0
b) \(\left(\frac{1}{2}-1\right):...:\left(\frac{1}{100}-1\right)=\frac{-1}{2}:\frac{-2}{3}:\frac{-3}{4}:...:\frac{-99}{100}\)
\(=\)\(\frac{-1}{2}.\frac{-3}{2}.....\frac{-100}{99}=\frac{-1}{2}.\left(-50\right)=25\)
\(=\frac{\frac{6}{5}:\left(\frac{6}{5}-\frac{5}{4}\right)}{\frac{8}{25}+\frac{2}{25}}+\frac{\frac{2027}{25}:\frac{9}{4}}{\left(\frac{38}{7}-\frac{9}{4}\right):\frac{267}{56}}\)
\(=\frac{\frac{6}{5}:\left(\frac{-1}{20}\right)}{\frac{2}{5}}+\frac{\frac{8180}{225}}{\frac{89}{28}:\frac{167}{56}}\)
\(=\frac{-12}{5}:\frac{2}{5}+\frac{8180}{225}:\frac{178}{167}\)
\(=-1+...\)ra số to vcl
Đề sai à ???
a)
\(\begin{array}{l}\frac{1}{9} - 0,3.\frac{5}{9} + \frac{1}{3}\\ = \frac{1}{9} - \frac{3}{{10}}.\frac{5}{9} + \frac{1}{3}\\ = \frac{1}{9} - \frac{3}{{2.5}}.\frac{5}{{3.3}} + \frac{1}{3}\\ = \frac{1}{9} - \frac{1}{6} + \frac{1}{3}\\ = \frac{2}{{18}} - \frac{3}{{18}} + \frac{6}{{18}}\\ = \frac{5}{{18}}\end{array}\)
b)
\(\begin{array}{l}{\left( {\frac{{ - 2}}{3}} \right)^2} + \frac{1}{6} - {\left( { - 0,5} \right)^3}\\ = \frac{4}{9} + \frac{1}{6} - \left( {\frac{{ - 1}}{2}} \right)^3\\ = \frac{4}{9} + \frac{1}{6} - \left( {\frac{{ - 1}}{8}} \right)\\ = \frac{4}{9} + \frac{1}{6} + \frac{1}{8}\\ = \frac{{32}}{{72}} + \frac{{12}}{{72}} + \frac{9}{{72}}\\ = \frac{{53}}{{72}}\end{array}\)
\(A=\left(1+\frac{1}{2}\right)x\left(1+\frac{1}{3}\right)x\left(1+\frac{1}{4}\right)x...x\left(1+\frac{1}{100}\right)\)
\(A=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x...x\frac{101}{100}\)
\(A=\frac{101}{2}\)
A = \(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{101}{100}\)
A = \(\frac{101}{2}\)
to khong biet cach trinh bay nhung ket qua =0