1+1+1+1+1+1+2+2+2+2+2+2+3+3+3+3+3+3+4x6+5x6+6x6+7x6+8x6+9x6+10x6+11x6+100x6000000000600000
a,(1/5-1/7):(30%-20%);b,(3-2 và1/2)x(1/2-1/3)
c,1/2x4+1/4x6+...+1/18x20;d,1/1+2+1/1+2+3+...+1/1+2+3+...+2018
h,1/1.6+2/6.11+2/11.16+2/16.21;g,1/1x2x3+1/2x3x4+...+1/18x19x20
C=1/(2x4)+1/(4x6)+...+1/(18x20)
2C=2/(2x4)+2/(4x6)+...+2/(18x20)
2C=1/2-1/4+1/4-1/6+....-1/20
2C= 1/2- 1/20
2C= 9/20
C= 9/20 x 1/2
C= 9/40
- Quên k auto súc vặc
a) 1/1x3 + 1/3x5 + 1/5x7 +...+ 1/2007x2009
b) 3^2/20x23 + 3^2/23x26 +...+ 3^2/77x80
c) 4/2x4 + 4/4x6 + 4/4x8 +...+ 4/2008x2010
d) 1/18 + 1/54 + 1/108 +...+ 1/990
e) B= 1 + 3 +3^2 +...+ 3^100
f) A= 2^0 + 2^1 + 2^2 +...+ 2^2010
g) S= 1 + 2 + 2^2 + 2^3 +...+ 2^2008 / 1 - 2^2009
chứng minh
a) 1/3^2+2/3^3+3/3^4+...+100/3^101<1/4
b) 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
c) 1/31+1/32+...+1/60=1/1x2+1/3x4+1/5x6+...+1/59x60
d) 1x3x5x7x...x49=26/2x27/2x28/2x...x50/2
1. tính tổng sau :
A= 1/ 1x3 + 1/ 3x5 + 1/ 5x7 + ...+ 1/ 99 x 101
S=2/1x6 + 2/ 6x11 + 2/ 11x6 + ...+ 2/ 96x11
2. Sắp xếp theo thứ tự từ bé đến lớn:
0,2 ; 7/3 ; 2 và 1/4 ; 11/5 ; 3/8; 2 và 1/7
3, tìm các cặp phân số = nhau
65/75;84/189;49/21;16/20;60/135;91/39;169/195
(X-2/3) x 1/6 = 18 1/3+2/3 x X = 2/5
7/11+4/11x13/7-4/11x6/7 4/9x11/15+4/9x4/15
\(\frac{4}{9}\cdot\frac{11}{15}+\frac{4}{9}\cdot\frac{4}{15}\)
\(=\frac{4}{9}\left(\frac{11}{15}+\frac{4}{15}\right)\)
\(=\frac{4}{9}\cdot1=\frac{4}{9}\)
\(\left(x-\frac{2}{3}\right).\frac{1}{6}=\frac{1}{8}\)
\(\left(x-\frac{2}{3}\right)=\frac{3}{4}\)
\(x=\frac{17}{12}\)
\(\left(x-\frac{2}{3}\right)\cdot\frac{1}{6}=18\)
\(\Rightarrow x-\frac{2}{3}=18:\frac{1}{6}=108\)
\(\Rightarrow x=108+\frac{2}{3}=\frac{326}{3}\)
\(\Rightarrow x=\frac{326}{3}\)
\(\frac{1}{3}+\frac{2}{3}\cdot x=\frac{2}{5}\)
\(\Rightarrow\frac{2}{3}\cdot x=\frac{2}{5}-\frac{1}{3}=\frac{1}{15}\)
\(\Rightarrow x=\frac{1}{15}:\frac{2}{3}=\frac{1}{10}\)
\(\Rightarrow x=0,1\)
Thực hiện phép tính :
a, 1+(1+2)+(1+2+3)+...+(1+2+3+..+100)
b,1/1x2+1/3x4+1/5x6+...+1/49x50
1.tính giá trị biểu thức
a)A=(6:3/5-1 và 1/6x6/7):(4 và 1/5x10/11+5 và 2/11)
b)B=(1 - 1/2)x(1-1/3)x(1-1/4)x..............x(1-1/2003)x(1-1/2004)
c)C=5 và 9/10:2/3-(2 và 1/3x 4 và 1/2)-2x2 và 1/3:2/4
B= 1/2 x 2/3 x 3/4 x ...........x 2002/2003 x 2003/2004
1 x 2 x 3 x 4 x .............x 2002 x 2003
2 x 3 x 4 x .............x 2003 x 2004
1
2004
Tính nhanh:
A= 1/2+1/2^2+1/2^3+....+1/2^100
B=3^2/2x4+3^2/4x6+3^2/6x8+....+3^2/198x200
C=\(\frac{\frac{2017}{1}+\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2017}}{\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}}\)
D=1x2+2x3+3x4+4x5+...+48x49
E=\(^{1^2+2^2+3^2+...+48^2}\)
F=1x49+2x48+3x47+...+48x2+49x1
B = \(\frac{3^2}{2.4}+\frac{3^2}{4.6}+\frac{3^2}{6.8}+...+\frac{3^2}{198.200}\)
B = \(\frac{3^2}{2}.\left(\frac{1}{2}-\frac{1}{4}\right)+\frac{3^2}{2}.\left(\frac{1}{4}-\frac{1}{6}\right)+\frac{3^2}{2}.\left(\frac{1}{6}-\frac{1}{8}\right)+...+\frac{3^2}{2}.\left(\frac{1}{198}-\frac{1}{200}\right)\)
B = \(\frac{3^2}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{198}-\frac{1}{200}\right)\)
B = \(\frac{9}{2}.\left(\frac{1}{2}-\frac{1}{200}\right)\)
B = \(\frac{9}{2}.\frac{99}{200}\)
B = \(\frac{891}{400}\)
D = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 48 x 49
3D = 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + 4 x 5 x 3 + ... + 48 x 49 x 3
3D = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 x ( 5 - 2 ) + 4 x 5 x ( 6 - 3 ) + ... + 48 x 49 x ( 50 - 47 )
3D = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + 4 x 5 x 6 - 3 x 4 x 5 + ... + 48 x 49 x 50 - 47 x 48 x 49
3D = 48 x 49 x 50
D = ( 48 x 49 x 50 ) : 3
D = 39200
E = 12 + 22 + 32 + ... + 482
E = 1 x 1 + 2 x 2 + 3 x 3 + ... + 48 x 48
E = 1 x ( 2 - 1 ) + 2 x ( 3 - 1 ) + 3 x ( 4 - 1 ) + ... + 48 x ( 49 - 1 )
E = 1 x 2 - 1 + 2 x 3 - 2 + 3 x 4 - 3 + ... + 48 x 49 - 49
E = ( 1 x 2 + 2 x 3 + 3 x 4 + ... + 48 x 49 ) - ( 1 + 2 + 3 + ... + 49 )
Ta tính được vế trong ngoặc thứ nhất là 39200 , còn vế trong ngoặc thứ hai là 1225
thay vào ta được :
E = 39200 - 1225
E = 37975
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\right)\)
\(\Rightarrow A=1-\frac{1}{2^{100}}\)
tìm y:
(2/2x4 + 2/4x6 + 2/6x8 + 2/8x10) x y = 1/3
`(2/(2xx4)+2/(4xx6)+2/(6xx8)+2/(8xx10))xxy=1/3`
`=>(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)xxy=1/3`
`=>(1/2-1/10)xxy=1/3`
`=>(5/10-1/10)xxy=1/3`
`=>4/10xxy=1/3`
`=>2/5xxy=1/3`
`=>y=1/3:2/5`
`=>y=1/3xx5/2`
`=>y=5/6`