Chứng minh
a)B=1/10+1/11+...+1/28 > 1
b)C=1/10.1/11+1/11.1/12+...+1/20.1/21 > 1/20
c)E=1/51+1/52+...+1/100 > 1
d)F=1/2^2+1/3^2+...+1/9^2
Chứng minh 2/5<F<8/9
e)H=1/31+1/32+...+1/60
Chứng minh 3/5<H<4/5
f)K=1/21+1/22+...+1/30>1/3
Chứng tỏ rằng:
1/10.1/11+1/11.1/12+...+1/20.1/21>1/20
1/10.1/11+1/11.1/12+1/12 ( 3 chấm ) 1/20.1/21
Chứng minh biểu thức trên bé hơn 1/20 (dấu chấm la dấu nhân nha m.n)
Mình cũng có bài đấy k bt lm
cho A=1/11+1/12+1/13+1/14+...+1/50
so sánh A với 1/2
cho B=1/50+1/51+1/52+...+1/98+1/99
chứng minh rằng b <1/2
cho C=1/10+1/11+1/12+...+1/99+1/100
chứng tỏ C >1
a, Ta có: \(A=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{50}=\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{30}\right)+\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{60}\right)\)
Nhận xét: \(\frac{1}{11}+\frac{1}{12}+....+\frac{1}{30}>\frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}=\frac{20}{30}=\frac{2}{3}\)
\(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{60}>\frac{1}{60}+\frac{1}{60}+...+\frac{1}{60}=\frac{20}{60}=\frac{1}{3}\)
\(\Rightarrow A>\frac{2}{3}+\frac{1}{3}=1>\frac{1}{2}\)
Vậy A > 1/2
b, Ta có: \(\frac{1}{50}>\frac{1}{100};\frac{1}{51}>\frac{1}{100};........;\frac{1}{99}>\frac{1}{100}\)
\(\Rightarrow B>\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}=\frac{50}{100}=\frac{1}{2}\)
Vậy B > 1/2
c, Ta có: \(C=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}=\frac{1}{10}+\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)\)
Nhận xét: \(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}>\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}=\frac{90}{100}=\frac{9}{10}\)
\(\Rightarrow C>\frac{1}{10}+\frac{9}{10}=\frac{10}{10}=1\)
Vậy C > 1
giup mik voi
B= 1/5 - 1/9 + 1/13 / 9/5 -1 + 9/13 + 10/7-10/11-10/17 / 12/7 - 12 /11 - 12/17
C=1/14 - 1/30 - 1/46 / 2/35 - 2/75 - 2/115 : 3/8 - 15/17 + 30/31 / 1/6 - 20/51 + 40/93
D= 1/100.99 - 1/99.98 - 1/98.97 - ........... - 1/3.2 - 1/2.1
E= ( 1+2+3+.......+100) . ( 1/3-1/5-1/7-1/9) . ( 6,3 .12 - 21 .3,6) / 1/2+1/3+1/4+..........+ 1/100
Nguyễn Đăng Duy ơi bài trên là tính nhanh hay tính vậy bạn .
Bài làm (không chắc)
B=1/5-1/9+1/13 / 9/5-1+9/13 + 10/7-10/11-10/17 / 12/7-12/11-12/17
=1/5:9/5-1/9:1+1/13:9/13 + 10/7:12/7-10/11:12/11-10/17:12/17
=1/9-1/9+1/9 + 5/6-5/6-5/6
=1/9-5/6
=39/54=13/18
Thực hiện phép tính:
A) 7/38 x 9/11 +7/38 x 4/11 -7/38 x 2/11
B) 5/31 x 21/25 + 5/31 x -7/10 - 5/31 x 9/20
C) ( -2/3 + 3/7 ) : 4/5 + (-1/3 + 4/7 ) : 4/5
D) 5/9 : ( 1/11 -5/22 ) + 5/9 : ( 1/15 - 2/3 )
E) 3/14 : 1/28 -13/21 : 1/28 + 29/42 : 1/28 - 8
F) ( -40/51 x 0,32 x17/20) : 64/75
Đây là dấu x ( là nhân ) mọi người nhé
mong mn giúp em ạ
A) 7/38 x 9/11 +7/38 x 4/11 -7/38 x 2/11
=7/38.(9/11+4/11-2/11)
=7/38
B) 5/31 x 21/25 + 5/31 x -7/10 - 5/31 x 9/20
=5/31.(21/25-7/10-9/20)
=5/31.(-31/100)
=-1/20
Câu1: Tính tổng 100 số hạng đầu tiên của các dãy sau
a)1/3 ; 1/15 ; 1/35 ;.......
b) 1/5; 1/45 ; 1/117 ; 1/221 ;..........
Câu 2 :Rút gọn
a) P= 1+(1+2)+(1+2+3)+...+(1+2+3+...+99+100) / (1x100+2x29+...+99x2+100x1)x2013
Câu3:
Q=4+3/5+...+3/95+3/97+3/99 / 1/1.99+1/3.97+1/5.95+...+1/95.5+1/97.3+1/99.1
Câu 4 :
A)Cho S=1/1! + 1/2!+ 1/3!+...+1/2012! . Chứng Minh Rằng S<2
b) Chứng minh rằng 9/10!+10/11!+11/12!+...+99/100! < 1/9!
Câu 5
a) Cho P=1-1/2+1/3-1/4+...+1/2011-1/2012
Q=1/1007+1/1008+..+1/2011+1/2012. Tính P: Q
b) Cho M= 1/2 - 3/4 + 5/6 - 7/8 +...+ 197/198 - 199/200 và N = 1/51+1/52+1/53+...+1/100
Tính N : M
Thanks bạn Đinh Tuấn Việt nhiều nah!!!!
a) 1/2 - 5/6 + 11/33 - 35/40
b) 2/3 . 1 3/4 - 8/9 - 17/51 - 1/5
c) 1/2 . 2 - 2 5/7 + 6/4 - 10/15
d) 1/6 . 1/11 + 4/11 . ( -1/6) + 8/11 . 1/6 + 1/6 . 6/11
e) -17 . (-23) + (-53) . 17 +17 . 14 + 17 .(-24)
f) -19,218 + (-82) .19 - 533 . 19 + (-19) . 167
g) 2/5 + 3/8 - 11/44 + 9/16
h) 4/10 - 1 5/6 . 2 + 7/8 -1/9
i ) 3. 1/5 - 2/8 - 12/36 + 15/9
k) 6/8 . 3 1/2 + 4 2/3 - 11/55 + 17/51
l ) 1/3 . 3 1/2 - 4 2/5 - 26/78 + 17/51
`@` `\text {Ans}`
`\downarrow`
`a)`
\(\dfrac{1}{2}-\dfrac{5}{6}+\dfrac{11}{33}-\dfrac{35}{40}\)
`=`\(\dfrac{1}{2}-\dfrac{5}{6}+\dfrac{1}{3}-\dfrac{7}{8}\)
`=`\(\dfrac{12}{24}-\dfrac{20}{24}+\dfrac{8}{24}-\dfrac{21}{24}\)
`= -21/24 = -7/8`
`b)`
\(\dfrac{2}{3}\cdot1\dfrac{3}{4}-\dfrac{8}{9}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(\dfrac{2}{3}\cdot\dfrac{7}{4}-\dfrac{8}{9}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(\dfrac{7}{6}-\dfrac{8}{9}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(\dfrac{5}{18}-\dfrac{17}{51}-\dfrac{1}{5}\)
`=`\(-\dfrac{1}{18}-\dfrac{1}{5}=-\dfrac{23}{90}\)
`c)`
\(\dfrac{1}{2}\cdot2-2\dfrac{5}{7}+\dfrac{6}{4}-\dfrac{10}{15}\)
`=`\(1-\dfrac{19}{7}+\dfrac{6}{4}-\dfrac{10}{15}\)
`=`\(-\dfrac{12}{7}+\dfrac{6}{4}-\dfrac{10}{15}\)
`=`\(-\dfrac{3}{14}-\dfrac{10}{15}=-\dfrac{37}{42}\)
`d) `
\(\dfrac{1}{6}\cdot\dfrac{1}{11}+\dfrac{4}{11}\cdot\left(-\dfrac{1}{6}\right)+\dfrac{8}{11}\cdot\dfrac{1}{6}+\dfrac{1}{6}\cdot\dfrac{6}{11}\)
`=`\(\dfrac{1}{6}\cdot\left(\dfrac{1}{11}-\dfrac{4}{11}+\dfrac{8}{11}+\dfrac{6}{11}\right)\)
`=`\(\dfrac{1}{6}\cdot\left(\dfrac{1-4+8+6}{11}\right)\)
`=`\(\dfrac{1}{6}\cdot1=\dfrac{1}{6}\)
`e)`
\(-17\cdot\left(-23\right)+\left(-53\right)\cdot17+17\cdot14+17\cdot\left(-24\right)\)
`= 17*(23-53+14-24)`
`= 17*(-40)`
`= -680`
`f)`
\(-19\cdot218+\left(-82\right)\cdot19-533\cdot19+\left(-19\right)\cdot167\)
`= 19*(-218-82-533-167)`
`= 19*(-1000)`
`= -19000`
`g)`
\(\dfrac{2}{5}+\dfrac{3}{8}-\dfrac{11}{44}+\dfrac{9}{16}\)
`=`\(\dfrac{2}{5}+\dfrac{3}{8}-\dfrac{1}{4}+\dfrac{9}{16}\)
`=`\(\dfrac{31}{40}-\dfrac{1}{4}+\dfrac{9}{16}\)
`=`\(\dfrac{21}{40}+\dfrac{9}{16}=\dfrac{87}{80}\)
`h)`
\(\dfrac{4}{10}-1\dfrac{5}{6}\cdot2+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(\dfrac{4}{10}-\dfrac{11}{6}\cdot2+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(\dfrac{4}{10}-\dfrac{11}{3}+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(-\dfrac{49}{15}+\dfrac{7}{8}-\dfrac{1}{9}\)
`=`\(-\dfrac{287}{120}-\dfrac{1}{9}=-\dfrac{901}{360}\)
`i )`
\(3\cdot\dfrac{1}{5}-\dfrac{2}{8}-\dfrac{12}{36}+\dfrac{15}{9}\)
`=`\(\dfrac{3}{5}-\dfrac{1}{4}-\dfrac{1}{3}+\dfrac{15}{9}\)
`=`\(\dfrac{7}{20}-\dfrac{1}{3}+\dfrac{15}{9}\)
`=`\(\dfrac{1}{60}+\dfrac{15}{9}=-\dfrac{33}{20}\)
`k)`
\(\dfrac{6}{8}\cdot3\dfrac{1}{2}+4\dfrac{2}{3}-\dfrac{11}{55}+\dfrac{17}{51}\)
`=`\(\dfrac{3}{4}\cdot\dfrac{7}{2}+\dfrac{14}{3}-\dfrac{1}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{21}{8}+\dfrac{14}{3}-\dfrac{1}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{175}{24}-\dfrac{1}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{851}{120}+\dfrac{17}{51}=\dfrac{297}{40}\)
`l )`
\(\dfrac{1}{3}\cdot3\dfrac{1}{2}-4\dfrac{2}{5}-\dfrac{26}{78}+\dfrac{17}{51}\)
`=`\(\dfrac{1}{3}\cdot\dfrac{7}{2}-\dfrac{22}{5}-\dfrac{1}{3}+\dfrac{17}{51}\)
`=`\(\dfrac{1}{3}\left(\dfrac{7}{2}-1\right)-\dfrac{22}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{1}{3}\cdot\dfrac{5}{2}-\dfrac{22}{5}+\dfrac{17}{51}\)
`=`\(\dfrac{5}{6}-\dfrac{22}{5}+\dfrac{17}{51}\)
`=`\(-\dfrac{107}{30}+\dfrac{17}{51}=-\dfrac{97}{30}\)
P/s: Bạn tách bài ra hỏi nhé! Và ghi đề rõ ràng chứ đừng ghi ntnay, nhiều bạn nhìn vào rất khó nhìn!
`# \text {KaizulvG}`
a)
` 1/2 - 5/6 + 11/33 - 35/40 `
`= 1/2 - 5/6 + 1/3 - 7/8 `
`= ( 1/2 - 5/6 ) + ( 1/3 - 7/8 ) `
`= ( 3/6 - 5/6 ) + ( 8/24 - 21/24 ) `
`= -2/6 + (-13)/24 `
`= -1/3 + (-13)/24 `
`= -8/24 + (-13)/24 `
`= -21/24 = -7/8 `
chứng minh
a) 1/2 < 1/51 + 1/52 +....+ 1/100 < 1
b) 7/12 < 1/21 + 1/22 + ...+ 1/40 < 5/6
Câu a:
Ta có: 1/51 > 1/100 ; 1/52>1/100 ..... ; 1/99>1/100
=> 1/51+1/52+...+1/100 > 1/100+1/100+.....+1/100 ( 50 số ) = 50/100=1/2 (1)
Ta lại có: 1/52<1/51; 1/53<1/51;....; 1/100<1/51
=> 1/51+1/52+....+1/100<1/51+1/51+.......+1/51 ( 50 số = 50/51<1 (2)
Từ (1) (2) => đpcm
Câu b làm tương tự :)
1) Tính: A= 2/4.7-3/5.9+2/7.10-3/9.13+..+2/301.304-3/401.405
2) Chứng minh rằng với mọi n thuộc số tự nhiên, n lớn hơn hoặc bằng 2: 3/9.14+3/14.19+...+3/(5n-1).(5n+4)<1/15
3) a) Cho A=9/5^2+9/11^2+9/17^2+...+9/305^2. Chứng minh A<3/4
b) Cho C=4/3+7/3^2+10/3^3+...+3n+1/3^n với số tự nhiên khác 0. Chứng minh rằng C<11/4
4) Tính: a) =1/2+1/2^2+1/2^3+...+1/2^100
b) B=1/3-1/3^2+1/3^3-1/3^4+...+1/3^99-1/3^100
5) So sánh: (1-1/2).(1-1/3).(1-1/4). ... .(1-1/20) với 1/21