Bài 1: tính Cho A= $\dfrac{1}{31} \dfrac{1}{32} \dfrac{1}{33} ........ \dfrac{1}{60}>\dfrac{7}{12}$ B=$\dfrac{1}{3^2} \dfrac{1}{3^2} \dfrac{1}{5^2} ..... \dfrac{1}{50^2}$ CMR B

2

NT

Nguyễn Thị Việt Hằng

27 tháng 3 2018

đơn giản quá!

NT

Nguyễn Thị Việt Hằng

27 tháng 3 2018

Bạn có bt làm bài 5 ko?

1. Cho N=$\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{60}$CMR $\dfrac{3}{5}< N< \dfrac{4}{5}$2. Cho M=$\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{29}{3^{29}}-\dfrac{30}{3^{30}}$CMR $M< \dfrac{3}{16}$3. Cho...

NL

Nguyễn Lê Hồng Thái

25 tháng 4 2021

0

BB

bảo bảo

14 tháng 9 2023

Điền dấu < ; > ; =

3$\dfrac{1}{5}-\dfrac{8}{3}...........\dfrac{17}{5}-2\dfrac{12}{5}$

$\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+....+\dfrac{1}{89}+\dfrac{1}{90}$ ..... $\dfrac{5}{6}$

#Toán lớp 5

0

KL

Khánh Linh

25 tháng 3 2017

BT5 : Chứng minh

2) $\dfrac{3}{5}< \dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+....+\dfrac{1}{59}+\dfrac{1}{60}< \dfrac{4}{5}$

2

HH

Hoang Hung Quan

25 tháng 3 2017

Giải:

Đặt $A=\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{59}+\dfrac{1}{60}$

Ta có:

$A=\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{59}+\dfrac{1}{60}$

$\Rightarrow A=\left(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{40}\right)+\left(\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{50}\right)+\left(\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{60}\right)$

Nhận xét:

$\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{40}< \dfrac{1}{30}+\dfrac{1}{30}+...+\dfrac{1}{30}=\dfrac{1}{3}$

$\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{50}< \dfrac{1}{40}+\dfrac{1}{40}+...+\dfrac{1}{40}=\dfrac{1}{4}$

$\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{60}< \dfrac{1}{50}+\dfrac{1}{50}+...+\dfrac{1}{50}=\dfrac{1}{5}$

$\Rightarrow A< \dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}=\dfrac{47}{60}< \dfrac{48}{60}=\dfrac{4}{5}$

$\Rightarrow A< \dfrac{4}{5}\left(1\right)$

Lại có:

$\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{40}>\dfrac{1}{40}+\dfrac{1}{40}+...+\dfrac{1}{40}=\dfrac{1}{4}$

$\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{50}>\dfrac{1}{50}+\dfrac{1}{50}+...+\dfrac{1}{50}=\dfrac{1}{5}$

$\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{60}>\dfrac{1}{60}+\dfrac{1}{60}+...+\dfrac{1}{60}=\dfrac{1}{6}$

$\Rightarrow A>\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}=\dfrac{37}{60}>\dfrac{36}{60}=\dfrac{3}{5}$

$\Rightarrow A>\dfrac{3}{5}\left(2\right)$

Từ $\left(1\right)$ và $\left(2\right)$

$\Rightarrow\dfrac{3}{5}< A< \dfrac{4}{5}$

Vậy $\dfrac{3}{5}< \dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{59}+\dfrac{1}{60}< \dfrac{4}{5}$ (Đpcm)

LT

Lâm &Team 6A

22 tháng 4 2018

Đặt $A=131+132+133+...+159+160A=131+132+133+...+159+160$

Ta có:

$A=131+132+133+...+159+160A=131+132+133+...+159+160$

$\RightarrowA=(131+132+...+140)+(141+142+...+150)+(151+152+...+160)\RightarrowA=(131+132+...+140)+(141+142+...+150)+(151+152+...+160)$

Nhận xét:

$131+132+...+140<130+130+...+130=13131+132+...+140<130+130+...+130=13$

$141+142+...+150<140+140+...+140=14141+142+...+150<140+140+...+140=14$

$151+152+...+160<150+150+...+150=15151+152+...+160<150+150+...+150=15$

$\RightarrowA<13+14+15=4760<4860=45\RightarrowA<13+14+15=4760<4860=45$

$\RightarrowA<45(1)\RightarrowA<45(1)$

Lại có:

$131+132+...+140>140+140+...+140=14131+132+...+140>140+140+...+140=14$

$141+142+...+150>150+150+...+150=15141+142+...+150>150+150+...+150=15$

$151+152+...+160>160+160+...+160=16151+152+...+160>160+160+...+160=16$

$\RightarrowA>14+15+16=3760>3660=35\RightarrowA>14+15+16=3760>3660=35$

$\RightarrowA>35(2)\RightarrowA>35(2)$

Từ $(1)(1)$ và $(2)(2)$

$\Rightarrow35<A<45\Rightarrow35<A<45$

Vậy $35<131+132+133+...+159+160<4535<131+132+133+...+159+160<45$

tính một cách hợp lí:a) $\dfrac{-5}{18}+\dfrac{32}{45}-\dfrac{9}{10}$b) $\left(\dfrac{-1}{4}+\dfrac{51}{33}-\dfrac{5}{3}\right)-\left(\dfrac{-15}{12}+\dfrac{6}{11}-\dfrac{42}{29}\right)$c) $1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}+4-\dfrac{1}{4}-3-\dfrac{1}{3}-2-\dfrac{1}{2}-1$ giải chi tiết giúp mình...

H

huongff2k3

18 tháng 7 2021

2

NL

Nguyễn Lê Phước Thịnh

18 tháng 7 2021

a) Ta có: $\dfrac{-5}{18}+\dfrac{32}{45}-\dfrac{9}{10}$

$=\dfrac{-25}{90}+\dfrac{64}{90}-\dfrac{81}{90}$

$=\dfrac{-42}{90}=-\dfrac{7}{15}$

b) Ta có: $\left(-\dfrac{1}{4}+\dfrac{51}{33}-\dfrac{5}{3}\right)-\left(-\dfrac{15}{12}+\dfrac{6}{11}-\dfrac{42}{29}\right)$

$=\dfrac{-1}{4}+\dfrac{17}{11}-\dfrac{5}{3}+\dfrac{5}{4}-\dfrac{6}{11}+\dfrac{42}{29}$

$=\dfrac{-5}{3}+\dfrac{42}{29}$

$=\dfrac{-145}{87}+\dfrac{126}{87}=\dfrac{-19}{87}$

c) Ta có: $1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}+4-\dfrac{1}{4}-3-\dfrac{1}{3}-2-\dfrac{1}{2}-1$

$=\left(1-1\right)-\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(2-2\right)-\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\left(3-3\right)-\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+4$

$=-1-1-1+4$

=1

Đúng(3)

H

huongff2k3

18 tháng 7 2021

a) Ta có: $\frac{- 5}{18} + \frac{32}{45} - \frac{9}{10}$

$= \frac{- 25}{90} + \frac{64}{90} - \frac{81}{90}$

$= \frac{- 42}{90} = - \frac{7}{15}$

b) Ta có: $(- \frac{1}{4} + \frac{51}{33} - \frac{5}{3}) - (- \frac{15}{12} + \frac{6}{11} - \frac{42}{29})$

$= \frac{- 1}{4} + \frac{17}{11} - \frac{5}{3} + \frac{5}{4} - \frac{6}{11} + \frac{42}{29}$

$= \frac{- 5}{3} + \frac{42}{29}$

$= \frac{- 145}{87} + \frac{126}{87} = \frac{- 19}{87}$

c) Ta có: $1 - \frac{1}{2} + 2 - \frac{2}{3} + 3 - \frac{3}{4} + 4 - \frac{1}{4} - 3 - \frac{1}{3} - 2 - \frac{1}{2} - 1$

$= (1 - 1) - (\frac{1}{2} + \frac{1}{2}) + (2 - 2) - (\frac{2}{3} + \frac{1}{3}) + (3 - 3) - (\frac{3}{4} + \frac{1}{4}) + 4$

$= - 1 - 1 - 1 + 4$

=1

Bài 1:Thực hiện phép tính (tính hợp lý nếu có thể)1) $\dfrac{8}{31}$ +$\dfrac{-12}{25}$ +$\dfrac{23}{31}$ +$\dfrac{-13}{25}$2) $\dfrac{1}{2}$ + $\dfrac{3}{4}$ - ( $\dfrac{3}{4}$ - $\dfrac{4}{5}$ )3) $\dfrac{7}{3}$ . $\dfrac{-5}{2}$ . $\dfrac{15}{21}$ .$\dfrac{4}{-5}$ 4)$\dfrac{1}{4}$ + $\dfrac{3}{4}$ : ( $-\dfrac{6}{7}$ )5) ($\dfrac{3}{29}$ - $\dfrac{1}{5}$ ) . $\dfrac{29}{3}$6) $\dfrac{5}{7}$ . $\dfrac{5}{11}$ + $\dfrac{5}{7}$...

NT

Nguyễn Thị Minh Huệ

25 tháng 9 2021

A=$\left[\dfrac{1\dfrac{11}{31}.4\dfrac{3}{7}-\left(15-6\dfrac{1}{3}.\dfrac{2}{19}\right)}{4\dfrac{5}{6}+\dfrac{1}{6}\left(12-5\dfrac{1}{3}\right)}.\left(-1\dfrac{14}{93}\right)\right].\dfrac{31}{50}$

#Toán lớp 7

0

VL

Vương Linh Đan

16 tháng 4 2023

2

NM

Nguyễn Minh Tiến

16 tháng 4 2023

1) = (8/31 + 23/31)+ ( -12/25+-13/25) = 1 + (-1) = 0
2) = 1/2 +3/4 -3/4 + 4/5 = 1/2 +4/5 = 13/10

3)= ( 7/3 x 15/21) x ( -5/2 x 4/-5 ) = ( 7/3 x 5/7 ) x 2 = 5/3 x 2 = 10/3

4) = 1/4 + 3/4 x -7/6 = 1/4 + -7/8 = -5/8

5)= 3/29 x 29/3 - 1/5 x 29/3 = 1 x 29/15 = 29/15

6)= 5/7 x ( 5/11 + 2/11 - 14/11) = 5/7 x -7/11 = -5 /11

7) = 11/12 x -1/8 + 11/12 x -3/16 - 11/12 = 11/12 x ( -1/8 + -3/16 - 1) = 11/12 x -21/16 = -77/64 ( mk ko chắc , bạn ấn máy tính để thử lại )

8) = 203/20 - 7/4 + 41/13 = 198/20 + 41/13 = 99/10 + 41/13 = 1697/130 ( câu này cứ lỏ lỏ kiểu gì ý :v )

DD

Đoàn Đức Sang

18 tháng 7 2023

1) = (8/31 + 23/31)+ ( -12/25+-13/25) = 1 + (-1) = 0
2) = 1/2 +3/4 -3/4 + 4/5 = 1/2 +4/5 = 13/10

3)= ( 7/3 x 15/21) x ( -5/2 x 4/-5 ) = ( 7/3 x 5/7 ) x 2 = 5/3 x 2 = 10/3

4) = 1/4 + 3/4 x -7/6 = 1/4 + -7/8 = -5/8

5)= 3/29 x 29/3 - 1/5 x 29/3 = 1 x 29/15 = 29/15

6)= 5/7 x ( 5/11 + 2/11 - 14/11) = 5/7 x -7/11 = -5 /11

7) = 11/12 x -1/8 + 11/12 x -3/16 - 11/12 = 11/12 x ( -1/8 + -3/16 - 1) = 11/12 x -21/16 = -77/64 ( mk ko chắc , bạn ấn máy tính để thử lại )

8) = 203/20 - 7/4 + 41/13 = 198/20 + 41/13 = 99/10 + 41/13 = 1697/130 ( câu này cứ lỏ lỏ kiểu gì ý :v )