3/1×2 + 3/3×5 + 3/5×7 + 3/7×9 +....+3/2015×2017+3/2017×2019
1 + 3 - 5 - 7 + 9 + 11 - 13 - 15 + ... + 2013 + 2015 - 2017 - 2019
1 + 3 - 5 - 7 + 9 + 11 - 13 - 15 + ... + 2013 + 2015 - 2017 - 2019
= (1 + 3 - 5 - 7) + (9 + 11 - 13 - 15) + ........ + (2013 + 2015 - 2017 - 2019)
= (- 8) + (- 8) + ......... + (- 8) có 275 số -8
= (- 8). 275
= -2200
1 + 3 - 5 - 7+ 9 + 11 - 13 - 15 + ... + 2013 + 2015 - 2017 - 2019
1 + 3 - 5 - 7 + 9 + 11 - 13 - 15 + ... + 2013 + 2015 - 2017 - 2019
1+3-5-7+9+11-13-15+...+2013+2015-2017-2019
=(1+3-5-7)+(9+11-13-15)+...+(2013+2015-2017-2019)
=(-8)+(-8)+...+(-8)
=(-8)x252,5
=-2020
Tính :A= [(2018/1)+(2017/2)+(2016/3)+(2015/4)+...+(4/2015)+(3/2016)+(2/2017)+(1/2018)]/[(2019/2)+(2019/3)+(2019/4)+(2019/5)+...+(2019/2015)+(2019/2016)+(2019/2017)+(2019/2018)+(2019/2019)]
TÍnh :
1 + 3 - 5 - 7 + 9 + 11 - 13 - 15 + ... + 2013 + 2015 - 2017 - 2019
A = 1 - 3 - 5 + 7 + 9 - 11 - 13 + ... - 2013 + 2015 + 2017 ( có 1009 số ; 1009 : 4 dư 1)
A = (1 - 3 - 5 + 7) + (9 - 11 - 13 + 15) + ... + (2009 - 2011 - 2013 + 2015) + 2017
A = 0 + 0 + ... + 0 + 2017
A = 2017
2+3-4+5+6-7+8+9-10+...+2015+2016-2017+2018+2019-2020+2021+2022
3+5-7-9+11+13-15-17+19...+2013-2015-2017+2019+2020
A = 3+5-7-9+11+13-15-17+19+.....+2011+ 2013-2015-2017+2019+2020
A=(3 +5-7-9)+(11+13-15-17)+....+(2011+2013-2015-2017)+2019+2020
xét dãy số : 3; 11; .....;2011
Dãy số trên có số số hạng : (2011 -3):8+1 = 252
Vậy tổng A là tổng 252 nhóm và 2019 + 2020
Mỗi nhóm có giá trị: 3 + 5 - 7 - 9 = -8
A = -8.252 + 2019 + 2020
A = 2023
Các bn ghi rõ cách giải nhé mk đang cần gấp lắm ai nhank mk tick cho cảm ơn
1: Tính nhanh
A= 1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
B= 1/1*3+1/3*5+1/5*7+...+1/2017*2019
C= 7/1*3+7/3*5+7/5*7+...+7/2017*2019
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(=1-\frac{1}{11}=\frac{10}{11}\)
\(\Rightarrow A=\frac{5}{11}\)
\(2B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)
\(=1-\frac{1}{2019}=\frac{2018}{2019}\Rightarrow B=\frac{1009}{2019}\)
\(\frac{2}{7}C=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)
\(=1-\frac{1}{2019}=\frac{2018}{2019}\Rightarrow C=\frac{2018}{2019}:\frac{2}{7}=\frac{7063}{2019}\)
Tính A =\(\dfrac{3^2-1}{5^2-1}.\dfrac{7^2-1}{^{ }9^2-1}......\dfrac{2015^2-1}{2017^2-1}.\dfrac{2017^2-1}{2019^2-1}\)
\(\frac{3^2-1}{5^2-1}.\frac{7^2-1}{9^2-1}......\frac{2015^2-1}{2017^2-1}.\frac{2017^2-1}{2019^2-1}\) \(\Rightarrow\frac{1}{3}.\frac{3}{5}......\frac{1007}{1009}.\frac{504}{505}\)=\(\frac{504}{505}\)