A=$\frac{1}{1.2} \frac{1}{2.3} \frac{1}{3.4} ... \frac{1}{2016.2017}$B=$\frac{1}{1.3} \frac{1}{3.5} \frac{1}{5.7} ... \frac{1}{2016.2017}$C=\(\frac{1}{2.4} \frac{1}{4.6} \frac{1}{6.8} ... \frac{1}...

9

BB

Bé bông 5d

7 tháng 4 2017

Lâm đi là: 35 phút +2 giờ 20phút =2 giờ 55 phút

TL

Trần Lê Khánh Nhật

7 tháng 4 2017

$A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2016.2017}$

$A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}$

$A=1-\frac{1}{2017}$

$A=\frac{2016}{2017}$

TP

Thu Phạm

8 tháng 9 2016

Tính tổng: $S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}$

1

VD

Võ Đông Anh Tuấn

8 tháng 9 2016

$S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}$

$=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)-\left(\frac{1}{2.4}-\frac{1}{4.6}-\frac{1}{6.8}-\frac{1}{8.10}\right)$

$=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{7}-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{8}-\frac{1}{10}\right)$

$=\frac{1}{2}\left(1-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)$

$=\frac{1}{2}.\frac{8}{9}-\frac{1}{2}.\frac{2}{5}$

$=\frac{4}{9}-\frac{1}{5}$

$=\frac{11}{45}$

TP

Thu Phạm

8 tháng 9 2016

Cảm ơn giúp bài nữa nha !!

LH

Lê Hằng Nga

7 tháng 9 2016

Tính tổng: $S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}$

4

MA

Minh Anh

7 tháng 9 2016

$A=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}$

$A=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)-\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)$

$A=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)-\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}\right)$

$A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)$

$A=\frac{1}{2}\left(1-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)$

$A=\frac{4}{9}-\frac{1}{5}=\frac{11}{45}$

HT

Hồ Thu Giang

7 tháng 9 2016

$S=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}$

$S=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)-\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\right)$

$S=\frac{1}{2}\left(1-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{10}\right)$

$S=\frac{1}{2}\left(1-\frac{1}{9}\right)-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10}\right)$

$S=\frac{1}{2}.\frac{8}{9}-\frac{1}{2}.\frac{2}{5}$

$S=\frac{4}{9}-\frac{1}{5}$

$S=\frac{11}{45}$

BT

Bùi Thị Ngọc Yến Nhi

24 tháng 10 2016

Gía trị biểu thức:

$\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+\frac{1}{5.7}+\frac{1}{6.8}+\frac{1}{7.9}+\frac{1}{8.10}$

14

DT

Đào Thùy Dương

24 tháng 10 2016

=$\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{2.4}+...+\frac{2}{8.10}\right)$

= $\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{2}-\frac{1}{4}+....+\frac{1}{8}-\frac{1}{10}\right)$

= $\frac{1}{2}.\left(1+\frac{1}{2}-\frac{1}{9}-\frac{1}{10}\right)$

=$\frac{29}{45}$

A

ahsnwuxnwixhs

24 tháng 10 2016

29/45 bạn nhé

MC

Mạnh Châu

8 tháng 8 2017

Thực hiện phép tinh sau:

$\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+\frac{1}{5.7}+\frac{1}{6.8}+\frac{1}{7.9}+\frac{1}{8.10}$

4

TP

Trần Phúc

8 tháng 8 2017

Ta có:

$\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+\frac{1}{5.7}+\frac{1}{6.8}+\frac{1}{7.9}+\frac{1}{8.10}$

$=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{8}-\frac{1}{10}\right)$

$=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}....+\frac{1}{7}-\frac{1}{9}\right)+\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{10}\right)$

$=\frac{1}{2}.\frac{8}{9}+\frac{1}{2}.\frac{2}{5}=\frac{1}{2}.\left(\frac{8}{9}+\frac{2}{5}\right)=\frac{1}{2}.\frac{58}{45}=\frac{29}{45}$

Đúng(1)

VT

Vũ Thùy Linh

9 tháng 9 2017

29/45 bạn ạ

H

๖ۣۜHυү♜(♜๖ۣۜTεαм♜๖ۣۜTαм♜๖ۣۜGĭá¢♜๖ۣۜ...

24 tháng 8 2019

$D=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+\frac{1}{5.7}-\frac{1}{6.8}+\frac{1}{7.9}-\frac{1}{8.10}$

Help me!~~~~~~~~~~~~~

3

R

Rinu

24 tháng 8 2019

Bài làm

D=ko viết lại đề

=1/1.3+1/1.5+1/5.7+1/7.9-1/2.4-1/4.6-1/6.8-1/8.10

=1+1/9-1-1/10

=10/9-9/10

=19/90

UT

╰❥ʄƖųơҳɛɬıŋɛ﹏❣ ( ๖ۣۜTεαм ๖ۣۜTαм ๖ۣ...

24 tháng 8 2019

=(1/1.3+...+1/7.9)-(1/2.4+...+1/8.10)

=2(1/1.3+...+1/7.9)-2(1/2.4+...+1/8.10)

=(2/1.3+...+2/7.9)-(2/2.4+...+2/8.10)

=(1-1/3+...+1/7-1/9)-(1/2-1/4+ +1/8-1/10)

=1-1/9-1/2+1/10

tự tính tiếp nhé

NN

Nguyễn Ngọc Khánh Vy

10 tháng 5 2017

$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2015.2016}+\frac{1}{2016.2017}$

1

FC

Five centimeters per second

10 tháng 5 2017

$\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}$

$=1-\frac{1}{2017}=\frac{2016}{2017}$

TD

Thành Đỗ

14 tháng 5 2017

Tính tổng sau : A= $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2016.2017}$

3

PT

Phạm Thị Hằng

14 tháng 5 2017

A = $1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}$

= $1-\frac{1}{2017}$

= $\frac{2016}{2017}$

14 tháng 5 2017

$A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2016}-\frac{1}{2017}$

$A=1+\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+...+\left(-\frac{1}{2016}+\frac{1}{2016}\right)-\frac{1}{2017}$

$A=1+0+0+...+0-\frac{1}{2017}$

$A=1-\frac{1}{2017}$

$A=\frac{2017}{2017}-\frac{1}{2017}$

$A=\frac{2016}{2017}$

Vậy: $A=\frac{2016}{2017}$

DT

Đặng Thị Cẩm Tú

26 tháng 1 2017

Rút gọn:

a/ $A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2000}$

b/ $B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{1998.1999.2000}$

c/ $C=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2006.2008}$

2

QD

Quang Duy

26 tháng 1 2017

a) $A=$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{2009.2010}$$

$A=$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{2009}-\frac{1}{2010}$$

A=1-$\frac{1}{2010}$=$\frac{2009}{2010}$

c)C=$\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+......+\frac{1}{2006.2008}$

C=$\frac{1}{2}$.($\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+..+\frac{1}{2006}-\frac{1}{2008}$)

C=$\frac{1}{2}$.($\frac{1}{2}-\frac{1}{2008}$)

C=$\frac{1}{2}$.$\frac{1003}{2008}$=$\frac{1003}{4016}$

Câu b mình chưa nghĩ ra

Chúc bạn học tốt!

HT

Hoàng Thị Ngọc Anh

26 tháng 1 2017

a) A = $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ...+ $\frac{1}{2009.2000}$

= 1 - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + ... + $\frac{1}{2009}$ - $\frac{1}{2000}$

= 1 - $\frac{1}{2000}$ = $\frac{1999}{2000}$

b) B = $\frac{1}{1.2.3}$ + $\frac{1}{2.3.4}$ + $\frac{1}{3.4.5}$ + ... + $\frac{1}{1998.1999.2000}$

= $\frac{1}{2}$ ( $\frac{2}{1.2.3}$ + $\frac{2}{2.3.4}$ + $\frac{2}{3.4.5}$ + ... + $\frac{2}{1998.1999.2000}$)

= $\frac{1}{2}$ ($\frac{1}{1.2}$ - $\frac{1}{2.3}$ + $\frac{1}{2.3}$ - $\frac{1}{3.4}$ + $\frac{1}{3.4}$ - $\frac{1}{4.5}$ + ... + $\frac{1}{1998.1999}$ - $\frac{1}{1999.2000}$)

= $\frac{1}{2}$ ($\frac{1}{1.2}$ - $\frac{1}{1999.2000}$)

= $\frac{1}{2}$ ($\frac{1}{2}$ - $\frac{1}{3998000}$)

= $\frac{1}{4}$ - $\frac{1}{7996000}$ = ?

c) C = $\frac{1}{2.4}$ + $\frac{1}{4.6}$ + $\frac{1}{6.8}$ + ... + $\frac{1}{2006.2008}$

= $\frac{1}{2}$ ($\frac{1}{2}$ - $\frac{1}{4}$) + $\frac{1}{2}$($\frac{1}{4}$ - $\frac{1}{6}$) + ... + $\frac{1}{2}$($\frac{1}{2006}$ - $\frac{1}{2008}$)

= $\frac{1}{2}$($\frac{1}{2}$ - $\frac{1}{4}$ + $\frac{1}{4}$ - $\frac{1}{6}$ + ... + $\frac{1}{2006}$ - $\frac{1}{2008}$)

= $\frac{1}{2}$($\frac{1}{2}$ - $\frac{1}{2008}$)

= $\frac{1}{2}$ . $\frac{1003}{2008}$ = $\frac{1003}{4016}$.

NN

Nga Nguyễn

4 tháng 12 2017

$A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2015.2016}$

$B=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2014.2016}$

Mấy bạn giúp mik nha

1

BT

Bùi Thế Hào

4 tháng 12 2017

$A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2015.2106}$

$A=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{2015}-\frac{1}{2016}\right)$

$A=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}$

$B=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2014.2016}=\frac{1}{4}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1007.1008}\right)$

=> $B=\frac{1}{4}.\left(\frac{1}{1}-\frac{1}{1008}\right)=\frac{1}{4}.\frac{1007}{1008}$

=> $B=\frac{1007}{4032}$