1/1x2+3/2x5+5/5x10+4/10x14+6/14x20
6 x5/3 7:8/4+1/3 2x5/8-1/2 3/7:5/6x1/4
10
\(\dfrac{23}{6}\)
\(\dfrac{3}{4}\)
\(\dfrac{9}{70}\)
6 x5/3=10 7:8/4+1/3=23/6 2x5/8-1/2=3/4 3/7:5/6x1/4=9/70
cho biểu thức : A= 1/1x2 + 3/2x5+9/5x14+23/14x37+15/37x52+1967/42x2619 chững minh A<1
Ta có A = \(\frac{1}{1.2}+\frac{3}{2.5}+\frac{9}{5.14}+\frac{23}{14.37}+\frac{15}{37.52}+\frac{1967}{52.2019}\)(sửa lại đề)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{14}+\frac{1}{14}-\frac{1}{37}+\frac{1}{37}-\frac{1}{52}+\frac{1}{52}-\frac{1}{2019}\)
\(=1-\frac{1}{2019}=\frac{2018}{2019}< 1\)
=> A < 1 (ĐPCM)
Tính nhanh:
a)1/3+2/3+5/12+4/3+1/12 b)3x5/6+5/6+2x5/6
c)___112x113+112x113_________
224x226+224x226
L= 1x2+2x4+3x6+4x8+5x10/3x4+6x8+9x12+12x16+15x20. tìm L
L=(1x2+2x1x2x2+3x1x2x3+4x1x2x4+5x1x2x5)/(3x4+2x3x4x2+3x3x4x3+4x3x4x4+5x3x4x5)
L=(1+2x2+3x3+4x4+5x5)(1x2)/(1+2x2+3x3+4x4+5x5)(3x4)
L=(1x2)/(3x2x2)
L=1/6
tính nhanh
1x2+2x43x6+4x8+5x10/3x4+6x8+9x12+12x16+15x20
Trong các phép tính sau, những phép tính nào làm đúng? ( CHỌN NHIỀU ĐÁP ÁN )
A 3/4 + 1/3 = 3+1 /4 + 3 = 4/7
B 7/9 - 1/3 = 7- 1/ 9- 3 = 6/6 = 1
C 6/7 x 2/5 = 6x2 / 2x5 = 12/35
D 5/6 : 1/3 = 5/6 x 3/1 = 5/2
1.so sánh
1/2:2/3......2/3:1/2 4/7:2/5......4/7:3/5
4/15:4/7......2/5x10/3 5/6......15/18-11/18
2.viết số thích hợp vào ô trống
2/3=..../18 7/9=49/.... ..../5=18/15
..../3=10/15 5/9=..../45 49/56=7/....
6/8=42/.... 2/9=..../63 49/56=..../8
`1)1/2:2/3 .... 2/3 : 1/2`
`=>1/2xx3/2 .... 2/3xx2`
`=>3/4 .... 4/3`
Vì `3/4 < 1` và `4/3>1`
`=>3/4<4/3`
__
`4/7:2/5 ... 4/7 : 3/5`
`=>4/7xx5/2....4/7xx5/3`
`=>20/14...20/21`
`=>10/7...20/21`
Vì `10/7>1` và `20/21<1`
`=>10/7>20/21`
__
`4/15:4/7....2/5xx10/3`
`=>4/15xx7/4...20/15`
`=>7/15...20/15`
Vì `7<20` nên `7/15<20/15`
__
`5/6...15/18-11/18`
`=>5/6...4/18`
Ta có : MSC : `18`
`5/6 = 15/18`
Vì `15>4` nên `5/6 > 4/18`
`2)2/3=(2xx6)/(3xx6)=12/18`
`7/9=(7xx7)/(9xx7)=49/63`
`6/5=(6xx3)/(5xx3)=18/15`
`2/3=(2xx5)/(3xx5)=10/15`
`5/9=(5xx5)/(9xx5)=25/45`
`49/56=(49:7)/(56:7)=7/8`
`6/8=(6xx7)/(8xx7)=42/56`
`2/9=(2xx7)/(9xx7)=14/63`
`49/56=(49:7)/(56:7)=7/8`
Tính
C=1x2+2x3+3x4+...+n(n+1)
D=1x4+2x5+3x6+...+99x102
\(C=1.2+2.3+3.4+...+n\left(n+1\right)\\ \Rightarrow3.C=1.2.3+2.3.3+3.4.3+..+n\left(n+1\right).3\\ \Rightarrow3.C=1.2.3+2.3.4-1.2.3+....+n\left(n+1\right)\left(n+2\right)-\left(n-1.n.\left(n+1\right)\right)\\ \Rightarrow3.C=n\left(n+1\right)\left(n+2\right)\\ \Rightarrow C=\dfrac{n\left(n+1\right)\left(n+2\right)}{3}\)
Cái D tính TT
tính
(2^2+1) x (2^2 -1) x (2^4 - 4^2)
(7^3+7^5) x (5^4+5^6) x (3^3 x 3-9^2)
2^2x5 [( 5^2 + 2^3) : 11] - 2^4 + 2 x 10^3
(2 ^ 2 + 1) x (2 ^ 2 - 1) x (2 ^ 4 - 4 ^ 2)
= (2 ^ 2 + 1) x (2 ^ 2 - 1) x ( 16 - 16 )
= (2 ^ 2 + 1) x (2 ^ 2 - 1) x 0
= 0
( 7 ^ 3 + 7 ^ 5) x (5 ^ 4 + 5 ^ 6) x ( 3 ^ 3 x 3 - 9 ^ 2)
= ( 7 ^ 3 + 7 ^ 5) x (5 ^ 4 + 5 ^ 6) x ( 3 ^ 4 - 3 ^ 4)
= ( 7 ^ 3 + 7 ^ 5) x (5 ^ 4 + 5 ^ 6) x 0
= 0
2 ^ 2 x 5 [( 5 ^ 2 + 2 ^ 3) : 11] - 2 ^ 4 + 2 x 10 ^ 3
= 4 x 5 [( 25 + 8 ) : 11] - 8 + 2 x 1000
= 20 ( 33 : 11) - 8 + 2000
= 20 x 3 - 8 + 2000
= 60 - 8 + 2000
= 2052