tinh (1-1/1+2)(1-1/1+2+3)...(1-1/1+2+3+...+2017)
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TP
2
PL
1
3 tháng 4 2019
\(B=\frac{2019}{1}+\frac{2018}{2}+\frac{2017}{3}+......+\frac{1}{2019}\)
\(=\left(\frac{2018}{2}+1\right)+\left(\frac{2017}{3}+1\right)+.....+\left(\frac{1}{2019}+1\right)+1\)
\(=\frac{2020}{2}+\frac{2020}{3}+\frac{2020}{4}+.....+\frac{2020}{2019}+\frac{2020}{2020}\)
\(=2020\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+......+\frac{1}{2020}\right)\)
\(=2020A\)
\(\Rightarrow\frac{A}{B}=\frac{A}{2020A}=\frac{1}{2020}\)
BK
0
TN
3
28 tháng 6 2016
\(\text{Ta có: }\)\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).........\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}........\frac{2015}{2016}.\frac{2016}{2017}\)
\(=\frac{1.2.3.4.....2015.2016}{2.3.4.5.....2016.2017}\)
\(=\frac{1}{2017}\)
PT
1
NL
2
KL
26 tháng 7 2017
A = (1 - 1/2) x (1 - 1/3) x (1 - 1/4) + ... + (1 - 1/2017) x (1 - 1/2018)
<=> A = 1/2 x 2/3 x 3/4 x ... x 2016/2017 x 2017/2018
<=> A = \(\dfrac{1\times2\times3\times...\times2016\times2017}{2\times3\times4\times...\times2017\times2018}\)
<=> A = \(\dfrac{1}{2018}\)
@Nguyễn Linh Ly
26 tháng 7 2017
\(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2017}\right)\left(1-\dfrac{1}{2018}\right)\)\(A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2016}{2017}.\dfrac{2017}{2018}\)
\(A=\dfrac{1.2.3....2016.2017}{2.3.4....2017.2018}\)
\(A=\dfrac{1}{2018}\)
KT
24 tháng 7 2018
a) \(35\times17+84\times35-35\)
\(=35\times\left(17+84-1\right)\)
\(=35\times100=3500\)
b) \(\frac{5}{2}\times\frac{1}{3}-\frac{1}{4}=\frac{5}{6}-\frac{1}{4}=\frac{7}{12}\)
c) \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{2017}\right)\left(1-\frac{1}{2018}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2016}{2017}.\frac{2017}{2018}\)
\(=\frac{1}{2018}\)
24 tháng 7 2018
a)35x17+84x35-35
=35x(17+84-1)
=35x100
=3500
b)5/2x1/3-1/4
=5/6-1/4
=7/12
c)(1-1/2)x(1-1/3)x(1-1/4)x......x(1-1/2018)
=1/2x2/3x3/4x...x2017/2018
=1/2018
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