tính A=1/2(1+1/1.3)(1+1/2.4)(1+3.5).....(1+1/2017.2018)
\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2017.2018}\right)\)
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Bạn ơi , xin lỗi mk ấn nhầm,đề là: \(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2017.2019}\right)\)nha !
Hình như sai đó, phải là:\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).....\left(1+\frac{1}{2016.2018}\right)\)
\(=\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}.....\frac{2016.2018+1}{2016.2018}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{2017^2}{2016.2018}\)
\(=\frac{\left(2.3.4....2017\right)\left(2.3.4....2017\right)}{\left(1.2.3....2016\right)\left(3.4.5.....2018\right)}\)
\(=\frac{2017.2}{2018.1}=\frac{2034}{2018}=\frac{2017}{1009}\)
A= 1/2 ( 1 + 1.3) ( 1 + 1/2.4) ( 1 + 3.5 ) ...............( 1 + 1/ 2015.2017)
tính m=(1+1/1.3)+(1+1/2.4)+(1+3.5).....(1+1/2014.2016)
tính :(1+1/1.3).(1+1/2.4)+(1+1/3.5)+...+(1+1/2014.2016)
luu y : dau /la phan cach giua mau so va tu so
Cho A = ( 1 + 1/1.3 ) ( 1 + 1/2.4 ) ( 1 + 1/3.5 ) .... ( 1 + 1/2017/2019 )
Chứng minh A > 2
Tính :
(1 + \(\dfrac{1}{1.3}\) ) . ( 1+\(\dfrac{1}{2.4}\) ) . (1+\(\dfrac{1}{3.5}\)) . ... . ( 1+\(\dfrac{1}{2019.2021}\))
Lời giải:
Gọi tích trên là $A$
Xét thừa số tổng quát: $1+\frac{1}{n(n+2)}=\frac{n(n+2)+1}{n(n+2)}=\frac{(n+1)^2}{n(n+2)}$
Thay $n=1,2,3....,2019$ ta có:
$A=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}....\frac{2020^2}{2019.2021}$
$=\frac{2^2.3^2...2020^2}{(1.3)(2.4)(3.5)...(2019.2021)}$
$=\frac{(2.3....2020)(2.3...2020)}{(1.2.3...2019)(3.4...2021)}$
$=2020.\frac{2}{2021}=\frac{4040}{2021}$
câu 1 tính
\(A=\dfrac{1}{2}\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{1}{3.5}\right)....\left(1+\dfrac{1}{2015.2017}\right)\)
\(A=\dfrac{1}{2}\left(2.\dfrac{2}{3}\right)\left(\dfrac{3}{2}.\dfrac{3}{4}\right)\left(\dfrac{4}{3}.\dfrac{4}{5}\right)....\left(\dfrac{2016}{2015}.\dfrac{2016}{2017}\right)\)
\(=\dfrac{2016}{2017}\)
Tính
A=(1-1/2).(1-1/3).(1-1/4).....(1-1/100)
B= (1+1/1.3).(1+1/2.4).(1+1/3.5).....(1+1/99.101)
Tính tổng S=1/1.3 + 1/2.4 + 1/3.5+....+1/4.9+ 1/8.10