c=(1+1/3*1)+(1+1/2*4).....(1+1/2014*2015)
tinh c
ai nhanh minh tick cho
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A)=vậy\(\frac{2014}{2015}+\frac{2015}{2014}>\frac{666665}{333333}.\)
bạn nhé
\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2015.2016}\)
\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2015}-\frac{1}{2016}\)
\(S=1-\frac{1}{2016}=\frac{2015}{2016}\)
\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-........+\frac{1}{2015}-\frac{1}{2016}\)
\(S=\frac{1}{1}-\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+......+\left(-\frac{1}{2015}+\frac{1}{2015}\right)-\frac{1}{2016}\)
\(S=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)
S = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/2014x2015 + 1/2015x2016
S = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2014 - 1/2015 + 1/2015 - 1/2016
S = 1 - 1/2016
S = 2015
\(1.2.3....2015-1.2.3....2014-1.2.3....2013.2014^2\)
\(=1.2.3...\left(2014+1\right)-1.2.3...\left(2014+1\right)\)
\(=0\)
\((2013\cdot2014\cdot2015)\cdot(1-\frac{1}{3}-\frac{1}{2}-\frac{1}{6})\)
\(=(2013\cdot2014\cdot2015)\cdot(\frac{6}{6}-\frac{2}{6}-\frac{3}{6}-\frac{1}{6})\)
\(=(2013\cdot2014\cdot2015)\cdot(\frac{6-2-3-1}{6})\)
\(=(2013\cdot2014\cdot2015)\cdot0=0\)
( 2013 × 2014 × 2015 ) × ( 1 - 1/3 - 1/2 - 1/6 )
= ( 2013 × 2014 × 2015 ) × ( 6/6 - 2/6 - 3/6 - 1/6)
= ( 2013 × 2014 × 2015 ) × 6 - 2 - 3 - 1/6
= ( 2013 × 2014 × 2015 ) × 0
= 0