cmr : 3/1^2 . 2^2 + 5/2^2 . 3^2 + 7/3^2 . 4^2 + ....+ 19/9^2 . 10^2 < 1
\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2+3^2}+...+\dfrac{19}{9^2-10^2}\)
\(=\) \(\dfrac{1}{1^2}-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+...+\dfrac{1}{9^2}-\dfrac{1}{10^2}\)
\(=\) \(1-\dfrac{1}{10^2}< 1\) ( đpcm )
CMR A=3/1^2+2^2+5/2^2+3^2+7/3^2+4^2+....19/9^2+10^2 <1
trả lời được thì mình kết bạn nha
Bài 1:
a) 8/7 - 5/11 : 8 b) 1 + 2/9 : 7/3 - 10/7 c) 11/3 - 2 : 7/3 + 4
Bài 2:
a) 9/4 - x = 5/11 : 1/2 b) 2/9 : x = 7/3 - 10/7
Bài 3:
\(\dfrac{1999x1998-1}{1997x1999+1998}\)
1:
a: =8/7-5/88=669/616
b: \(=1+\dfrac{2}{9}\cdot\dfrac{3}{7}-\dfrac{10}{7}=1+\dfrac{2}{21}-\dfrac{10}{7}\)
\(=\dfrac{21+2-30}{21}=\dfrac{-7}{21}=\dfrac{-1}{3}\)
c: \(=\dfrac{11}{3}-\dfrac{6}{7}+4=\dfrac{77-18+84}{21}=\dfrac{143}{21}\)
Bài 2:
a: =>9/4-x=5/11*2=10/11
=>x=9/4-10/11=59/44
b: =>2/9:x=19/21
=>x=2/9:19/21=14/57
Bài 1: Tính
a) 1/3 + 1/5 - 1/4 b) 7/8 - ( 1/4 + 2/5 ) c) 5/11 - ( 3/5 - 6/11 )
Bài 2: Tìm x
a) x + 2/5 = 1/2 b) x + 3/7 = 2/5 + 3/10 c) 19/20 - x = 8/5 - 3/4
Bài 3: Tìm số tự nhiên x, biết:
a ) 4/7 < x < 1/2 + 10/3 b) 3/10 + 8/5 < x < 2/5 + 5
Giúp mình nha ^^ Ai nhanh mình Tick !!!!!!!!!❤❤
Bài 1 tìm x biết
a> x=7/25+-1/5
b> x=5/11+4/-9
c> x/3=2/3+-1/7
d> x/5=5/6+-19/30
e> x/6=3/2+-7/15
Bài 2 cộng các phân số sau
a> -650/1430+588/686
b> 2004/2010+8/-670
Bài 3 tìm x biết
a> -5/13+-4/13 < x/13 < 2/13+-7/13
b> 3/2+-1/3 <x/6 < 1/9+31/18
c> -5/19+3/19 < x/19 bé hơn hoặc bằng 13/19+-11/19
d> -7/8+5/6 bé hơn hoặc bằng x/24 bé hơn hoặc bằng 5/8+-5/12
Bài 1 :
\(a)x=\frac{7}{25}+\left(-\frac{1}{5}\right)\)
\(x=\frac{2}{25}\)
\(b)x=\frac{5}{11}+\left(\frac{4}{-9}\right)\)
\(x=\frac{1}{99}\)
Mấy câu kia dễ tự làm :>
bài 1: cho A=3 + 3^2 + 3^3 +......+3^60. Chứng minh rằng
a)A chia hết 4 b)A chia hết 13
bài 2: CMR: (12a + 36b) chia hết 12 với a,b thuộcN
bài 3:cho a,b,c thuộc N và (111a + 23b) chia hết 12
CMR: (9a + 13b) chia hết cho 12
bài 4: CMR
a) 5 + 5^2 + 5^3 chia hết cho 5
b) 2^9 + 2^10 + 2^11 + 2^12 chia hết cho 15
c) 10^11 + 8 chia hét cho 3
d) 3^20 + 3^19 - 3^18 chia hết 11
bài 5: cho A = 8n + 111....1( n chữ số 1)
CMR: A chia hết 9
b)=3^1+(3^2+3^3+3^4)+(3^5+3^6+3^7)+....+(3^58+3^59+3^60)
=3^1+(3^2.1+3^2.3+3^2.9)+(3^5.1+3^5.3+3^5.9)+......+(3^58.1+3^58.3+3^58.9)
=3^1+3^2.(1+3+9)+3^5.(1+3+9)+.....+3^58.(1+3+9)
=3+3^2.13+3^5.13+.........+3^58.13
=3.13.(3^2+3^5+....+3^58)
vi tich tren co thua so 13 nen tich do chia het cho 13
=
bai1
a) A=(31+32)+(33+34)+...+(359+360)
=(3^1.1+3^1.3)+...+(3^59.1+3^59.2)
=3^1.(1+3)+...+3^59.(1+3)
=3^1.4+....+3^59.4
=4.(3^1+...+3^59)
vi tich tren co thua so 4 nen tich do chia het cho 4
Bài 2:(12a + 36b) = (12a + 12 x 3 x b) = 12( a + 3b)chia hết cho 12
Tính
a) 4/3*7 + 4/7*11 + 4/11*15 + 4/15*19 + 4/19*23 + 4/23*27
b) 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 +1/6*7
c) 2/3*5 + 2/5*7 + 2/7*9 + 2/9*11 + 2/11*13 + 2/1*2 + 2/2*3 + 2/3*4 + 2/8*9 + 2/9*10
a)\(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{23.27}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)
b)\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
c)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{1.2}+\frac{2}{2.3}+...+\frac{2}{9.10}=\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)+2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{3}-\frac{1}{13}+2\left(1-\frac{1}{10}\right)=\frac{10}{39}+\frac{9}{5}=\frac{401}{195}\)
CMR: 3/1^2. 2^2 +5/2^2. 3^2+..........+19/9^2. 10^2 < 1
\(\frac{3}{1^2\cdot2^2}+\frac{5}{2^2\cdot3^2}+...+\frac{19}{9^2\cdot10^2}\)\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+...+\frac{1}{9^2}-\frac{1}{10^2}=1-\frac{1}{10^2}=\frac{99}{100}\)<1
