(2013*2014+2014*2015+201582016)*(1+1/3-1 1/3)
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\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{\frac{5}{2012}+\frac{5}{2013}-\frac{5}{2014}}-\frac{\frac{2}{2013}+\frac{2}{2014}-\frac{2}{2015}}{\frac{3}{2013}+\frac{3}{2014}-\frac{3}{2015}}\)
=\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{5\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}\right)}-\frac{2\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}{3\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=-\frac{7}{15}\)
Tính
1 1/3 là hỗn số đúng không ta? :))
\(\left(2013\times2014+2014\times2015+2015\times2016\right)\times\left(1+\frac{1}{3}-1\frac{1}{3}\right)\)
\(=\left(2013\times2014+2014\times2015+2015\times2016\right)\times\left(1\frac{1}{3}-1\frac{1}{3}\right)\)
\(=\left(2013\times2014+2014\times2015+2015\times2016\right)\times0\)
\(=0\)
( 2013 x 2014 +2014 x 2015 + 2015 x 2016 ) x ( 1 + 1/3 - 1 - 1/3 )
= ( 2013 x 2014 + 2014 x 2015 + 2015 x 2016 ) x 0
= 0
Chứng minh \(\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\) rồi áp dụng với n = 1,2,....,2014
\(A=\left[1+\left(-2\right)\right]+\left[3+\left(-4\right)\right]+....+\left[2013+\left(-2014\right)+2015\right]\)
\(A=\left(-1\right)+\left(-1\right)+....+\left(-1\right)+2015\left(\text{1007 số hạng }\left(-1\right)\right)=1008\)
d)(2013 × 2014 + 2014 × 2015 + 2015 × 2016) × (1 + 1/3 - 1 1/3)
=(2013 × 2014 + 2014 × 2015 + 2015 × 2016) × (1 1/3 - 1 1/3)
=(2013 × 2014 + 2014 × 2015 + 2015 × 2016) × 0
= 0