4.6 * x + 3.4 * x = 0.8
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NH
2
BN
6 tháng 5 2017
\(\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot\frac{4^2}{4\cdot5}\cdot\frac{5^2}{5\cdot6}=\frac{1^2}{1\cdot6}=\frac{1}{6}\)
lan sau nho ghi de cho dung nha bn
6 tháng 5 2017
\(\frac{1.1.2.2.3.3.4.4.5.5}{1.2.2.3.3.4.4.5.5.6}\)=\(\frac{\left(1.2.3.4.5\right).\left(1.2.3.4.5\right)}{\left(1.2.3.4.5\right)\left(2.3.4.5.6\right)}=\frac{1}{6}\)
9 tháng 6 2023
(1,4 + 2,6) x 2 = 4 x 2 = 8
70 : (4,6 + 3,4 - 1) = 70 : 7 = 10
LM
Lê Minh Vũ
VIP
9 tháng 6 2023
\(\left(1,4+2,6\right)\times2\)
\(=4\times2=8\)
\(70\div\left(4,6+3,4-1\right)\)
\(=70\div7=10\)
8 tháng 1 2021
Bài 1:
a) Ta có: \(\dfrac{7^4\cdot3-7^3}{7^4\cdot6-7^3\cdot2}\)
\(=\dfrac{7^3\cdot\left(7\cdot3-1\right)}{7^3\cdot2\left(7\cdot3-1\right)}\)
\(=\dfrac{1}{2}\)
c) Ta có: \(E=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{100}}\)
\(\Leftrightarrow\dfrac{1}{3}\cdot E=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{101}}\)
\(\Leftrightarrow E-\dfrac{1}{3}\cdot E=1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{100}}-\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{101}}\right)\)
\(\Leftrightarrow E\cdot\dfrac{2}{3}=1-\dfrac{1}{3^{101}}\)
\(\Leftrightarrow E=\dfrac{3-\dfrac{3}{3^{101}}}{2}=\dfrac{1-\dfrac{1}{3^{100}}}{2}\)
HH
1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
14 tháng 5 2023
A =\(\dfrac{7}{3.4}\) + \(\dfrac{7}{4.6}\) + \(\dfrac{7}{5.8}\) + \(\dfrac{7}{6.10}\)+...+\(\dfrac{7}{60.118}\)
A = \(\dfrac{2.7}{2.3.4}\) + \(\dfrac{2.7}{2.4.6}\)+\(\dfrac{2.7}{2.5.8}\) + \(\dfrac{2.7}{2.6.10}\)+...+\(\dfrac{2.7}{2.60.118}\)
A = 7.(\(\dfrac{2}{6.4}\)+\(\dfrac{2}{8.6}\)+\(\dfrac{2}{10.8}\)+\(\dfrac{2}{12.10}\)+...+\(\dfrac{2}{120.118}\))
A = 7.(\(\dfrac{2}{4.6}\)+\(\dfrac{2}{6.8}\)+\(\dfrac{2}{8.10}\)+\(\dfrac{2}{10.12}\)+...+\(\dfrac{2}{118.120}\))
A = 7.(\(\dfrac{1}{4}-\dfrac{1}{6}\)+ \(\dfrac{1}{6}-\dfrac{1}{8}\) +\(\dfrac{1}{8}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{12}\) +...+ \(\dfrac{1}{118}\) - \(\dfrac{1}{120}\))
A = 7.( \(\dfrac{1}{4}\) - \(\dfrac{1}{120}\))
A = 7.\(\dfrac{29}{120}\)
A = \(\dfrac{203}{120}\)
30 tháng 4 2015
\(\frac{2.4+4.6+6.8+...+98.100}{1.2+2.3+3.4+...+49.50}=\frac{4.\left(1.2+2.3+3.4+...+49.50\right)}{1.2+2.3+3.4+...+49.50}=\frac{4}{1}=4\)
NH
3
31 tháng 1
\(A=1\cdot2+2\cdot3+...+151\cdot152\)
\(=1\left(1+1\right)+2\left(1+2\right)+...+151\left(1+151\right)\)
\(=\left(1+2+3+...+151\right)+\left(1^2+2^2+...+151^2\right)\)
\(=\dfrac{151\left(151+1\right)}{2}+\dfrac{151\left(151+1\right)\left(2\cdot151+1\right)}{6}\)
\(=151\cdot76+\dfrac{151\cdot152\cdot303}{6}\)
\(=151\cdot76+151\cdot7676=1170552\)
\(C=2\cdot4+4\cdot6+...+2024\cdot2026\)
\(=2\cdot2\left(1\cdot2+2\cdot3+...+1012\cdot1013\right)\)
\(=4\left[1\left(1+1\right)+2\left(1+2\right)+...+1012\left(1+1012\right)\right]\)
\(=4\left[\left(1+2+...+1012\right)+\left(1^2+2^2+...+1012^2\right)\right]\)
\(=4\left[1012\cdot\dfrac{1013}{2}+\dfrac{1012\left(1012+1\right)\left(2\cdot1012+1\right)}{6}\right]\)
\(=4\left[506\cdot1013+345990150\right]\)
\(=1386010912\)
\(M=1^2+2^2+...+2024^2\)
\(=\dfrac{2024\left(2024+1\right)\cdot\left(2\cdot2024+1\right)}{6}\)
\(=2024\cdot2025\cdot\dfrac{4049}{6}\)
=2765871900
\(N=1^3+2^3+...+100^3\)
\(=\left(1+2+3+...+100\right)^2\)
\(=\left[\dfrac{100\left(100+1\right)}{2}\right]^2\)
\(=\left[50\cdot101\right]^2=5050^2\)
\(Q=1^3+2^3+...+2024^3\)
\(=\left(1+2+3+...+2024\right)^2\)
\(=\left[\dfrac{2024\left(2024+1\right)}{2}\right]^2\)
\(=\left[1012\left(2024+1\right)\right]^2\)
\(=2049300^2\)
NL
1
12 tháng 3 2017
gọi tổng của 1+2+3+4+...+79 là M
2+3+4+...+80 là N
ta có A = M.N
từ 1 đến 79 hay từ 2 đến 80 có (79-1) chia 1 + 1=79
M = (79+1).79 chia 2= 3160
N = (80+2).79chia 2= 3239
A = 3160 .3239 = 10235240
YY
1
21 tháng 3 2015
a,ta thay hai so o duoi mau so la hai sop tu nhien lien tiep khoang cach chinh bang 1
ta co 1/3-1/4+1/4-1/5+.............................+1/20-1/21
ta co =1/3-1/21 vi co cac so doi to da the hien tren
=2/7
b vi khoang cach duoi mau kac tu mau la 2 con tu la 1 vay nhan 2 vao ca day so ta duoc
2/4.6+2/6.8+..............................+2/30.32
bay gio khoang cach duoi mau bang tu ta co
1/4-1/6+1/6-1/8+............................+1/30-1/32
nhu tren ta co =(1/4-1/32):2=7/64
NT
2
12 tháng 8 2018
B = 1.2+2.3+3.4+...+99.100
B=1.100
B=100
C=1.3+2.4+3.5+4.6+...+9.11
C=1.(2+1)+2.(3+1)+3.(4+1)+4.(5+1)+...+9.(10+1)
C=1.2+1+2.3+1+3.4+1+4.5+1+...+9.10+1
C=(1.2+2.3+3.3+4.5+...+9.10)+(1+1+1+1+..+1)
C=1.10+10
C=10+10
C=20
12 tháng 8 2018
a) B = 1.2+2.3+3.4+..+99.100
=>3B=1.2.3+2.3.3+3.4.3+...+99.100.3
3B = 1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5-2.3.4+...+99.100.101-98.99.100
3B = (1.2.3+2.3.4+3.4.5+..+99.100.101) - (1.2.3+2.3.4+...+98.99.100)
3B = 99.100.101
\(B=\frac{99.100.101}{3}=333300\)
b) C = 1.3+2.4+3.5+4.6+...+9.11
C = (2-1).(2+1)+(3-1).(3+1) + (4-1).(4+1)+(5-1).(5+1)+...+(10-1).(10+1)
C = 22 - 1 + 32 - 1 + 42 - 1 + 52 - 1 +...+102 - 1
C = (22+32+42+52+...+102) -(1+1+...+1)
...
\(4,6\times x+3,4\times x=0,8\\ x\times\left(4,6+3,4\right)=0,8\\ x\times8=0,8\\ x=0,8:8\\ x=0,1\)
x.(4,6+3,4) = 0,8
x.8 = 0.8
x = 0,8 : 8
x = 0,1