Bài 320:
a) 25/42- 20/63 = 75/126 - 40/126 = 35/126 = 5/18
b) 9/50 - 13/75 -1/6= 27/150 - 26/150 - 25/150 = -24/150 = -5/25
c) 2/15 - 2/65 - 4/39 = 26/195 - 6/195 - 20/195 = 0
Bài 321:
a) x+7/12= 17/18 - 1/9
=> x+7/12 = 5/6
=> x= 5/6 - 7/12
=> x= 1/4
Vậy x = 1/4
b) 29/30 - (13/23 +x) = 7/69
=> 13/23 +x = 29/30 -7/69
=> 13/23 +x = 199/230
=> x = 199/230 - 13/23
=> x= 3/10
Vậy x= 3/10
Bài 324:
Ta có: m/2 - 2/n = 1/2
=> nm/2n - 4/2n = 1/2
=> (mn-4)/2n= 1/2
=> 2mn - 8 = 2n
=> 2mn - 2n = 8
=> 2n(m-1) = 8
=> 2n ; m-1 ∈Ư(8)
=> 2n; m-1 ∈{ 1; 2;4;8; -1; -2; -4; -8}
Lập bảng xét giá trị là ra nha bạn
Bài 327:
a) A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5+.....+ 1/49.50
A= 1/1 -1/2 + 1/2 -1/3 + 1/3 -1/4-........+ 1/49 -1/50
A= 1 -1/50
A= 49/50
Vậy A= 49/50
b) B= 2/3.5 + 2/5.7 + 2/7.9 +..........+ 2/37.39
B= 1/3 - 1/5 + 1/5 -1/7 + 1/7 -1/9+....+ 1/37 - 1/39
B = 1/3 - 1/39
B= 4/13
Vậy B= 4/13
c) C= 3/4.7 + 3/7.10 + 3/10.13 +......+3/73.76
C= 1/4 -1/7 + 1/7- 1/10 + 1/10 -1/13 +....+ 1/73 - 1/76
C= 1/4 - 1/76
C= 9/38
Vậy C= 9/38
Bài 328:
Đặt A= 4/5.9 + 4/9.13 + 4/13.17+...+ 4/41.45
A= 1/5 - 1/9 + 1/9 - 1/13 + 1/13 -1/17+....+ 1/41 - 1/45
A=1/5 - 1/45
A= 8/45
=> x+8/45 = -37/45
=> x= -37/45 - 8/45
=> x= -1
Vậy x= -1
Bài 329:
S= 3/1.4 + 3/4.7 + 3/7.10 + ....+ 3/n(n+3)
S= 1/1 -1/4 + 1/4 - 1/7 + 1/7 - 1/10 +...+ 1/n - 1/n+3
S= 1 -1/n+3
Vì 1= 1 => 1 - 1/n+3 < 1 hay S <1
Vậy S <1
Bài 330:
Ta có: 1/2^2 < 1/1.2 ; 1/3^2 < 1/2.3; ..... ; 1/9^2 < 1/8.9
=> 1/2^2 + 1/3^2 + 1/4^2+.........+ 1/9^2 < 1/1.2 + 1/2.3 + .... + 1/8.9
=> S < 1/1 -1/2 + 1/2 -1/3 +....+ 1/8- 1/9
=>S < 1/1 -1/9
=> S < 8/9 (1)
Lại có: 1/2^2 > 1/2.3 + 1/3^2 > 1/3.4 ; .........; 1/9^2 < 1/9.10
=> 1/2^2 + 1/3^2 + 1/4^2+.........+ 1/9^2 > 1/2.3 + 1/3.4 +...+ 1/9.10
=> S > 1/2 -1/3 + 1/3 -1/4 +....+ 1/9-1/10
=> S > 1/2 -1/10 = 2/5 (2)
Từ (1) và (2) => 8/9 > S > 2/5
Vậy 8/9 > S > 2/5
