\(1\cdot\frac{1}{15}\cdot1\frac{1}{16}\cdot1\frac{1}{17}\cdot....\cdot1\frac{1}{2016}\cdot1\frac{1}{2017}\)

\(=\frac{1}{15}\cdot\frac{17}{16}\cdot\frac{18}{17}\cdot....\cdot\frac{2017}{2016}\cdot\frac{2018}{2017}\)

\(=\frac{1}{15}\cdot\frac{1}{16}\cdot2018\)

Dấu "." là dấu nhân nhé bn! phần còn lại bn làm tiếp nha

ĐẶT BIỂU THỨC TRÊN LÀ M

TA CÓ \(2M=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{64}\)

\(\Rightarrow2M-M=1+\frac{1}{2}+\frac{1}{4}+..+\frac{1}{64}-\frac{1}{2}+\frac{1}{4}+..+\frac{1}{128}\)

\(\Rightarrow M=1+\frac{1}{28}\)

A= \(\frac{1}{2}\)+\(\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)

2A=2(\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\))

    =1+\(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)

2A-A= (\(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)) -(\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\))

A=1-\(\frac{1}{128}\)

A=\(\frac{127}{128}\)

Bài làm

a) 27x38+62x37-27x90

=27x38+62x(27+10)-27x90

=27x38+62x27+62x10-27x90

=27x(38+62-90)+620

=27x10+620

=270+620

=890

b)1994x867+1995x133

=1994x867+(1994+1)x133

=1994x867+1994x133+1x133

=1994x(867+133)+133

=1994x1000+133

=1994000+133

=1994133

Chúc học tốt!

a: 27x38+62x37-27x90

=62x37-27x(90-38)

=62x37-27x52

=2294-1404

=890

b: 1994x867+1995x133

=1994x867+1994x133+133

=1994x(867+133)+133

=1994x1000+133

=1994000+133

=1994133

a)  \(\left(\frac{4}{3}-\frac{4}{6}\right)+\left(\frac{4}{6}-\frac{4}{9}\right)+\left(\frac{4}{9}-\frac{4}{10}\right)+\left(\frac{4}{12}-\frac{4}{15}\right)\)

    \(=\frac{4}{15}-\frac{4}{3}=\frac{-16}{15}\)

C) bạn chỉ ần bỏ các số giống nhau thôi nhé

   = 1

b) 

Do con lợn TNT học giỏi không biết làm phần b ) .  , Trắng sẽ giúp bạn :

1/2 + 1/6 + 1/12 + ...+ 1/110

= 1/1.2 + 1/2. 3 + 1/3 . 4 + ... + 1/10 . 11 

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/10 - 1/11

= 1 - 1/11 

= 10/11

B = (1999x1998 + 1998x1997)x(1+1/2: 1 1/2 - 11/3)

B = (1999x1998 + 1998x1997)x(1+1/2:3/2-4/3)

B = (1999x1998 +1998 x1997) x (1+1/2x2/3 - 4/3)

B = (1999 x 1998 + 1998 x 1997) x(1+1/3 - 4/3)

B = (1999 x 1998 + 1998 x 1997) x (4/3 - 4/3)

B = (1999 x 1998 + 1998 x 1997) x 0

B = 0

B = (1999x1998 + 1998x1997)x(1+1/2: 1 1/2 - 11/3)

B = (1999x1998 + 1998x1997)x(1+1/2:3/2-4/3)

B = (1999x1998 +1998 x1997) x (1+1/2x2/3 - 4/3)

B = (1999 x 1998 + 1998 x 1997) x(1+1/3 - 4/3)

B = (1999 x 1998 + 1998 x 1997) x (4/3 - 4/3)

B = (1999 x 1998 + 1998 x 1997) x 0

B = 0

Đặt biểu thức trên là A ta có:

A = \(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{12}\)+ \(\frac{1}{24}\)+ \(\frac{1}{48}\)+ \(\frac{1}{96}\)

A x 3 = \(1\)+ \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ \(\frac{1}{16}\)+ \(\frac{1}{32}\)

A x 3 = \(1\)+ \(1\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{8}\)+ \(\frac{1}{8}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{32}\)

A x 3 = 2 - \(\frac{1}{32}\)= \(\frac{63}{32}\)

A = \(\frac{63}{32}\): 3 = \(\frac{63}{96}\)

bằng 1

7096320

k nhé

thanks

\(A=\frac{2019}{2}+\frac{2019}{6}+\frac{2019}{12}+....+\frac{2019}{2018.2019}\)

   \(=\frac{2019}{1}.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2018.2019}\right)\)

   \(=\frac{2019}{1}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\right)\)

   \(=\frac{2019}{1}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+....+\frac{1}{2018}-\frac{1}{2019}\right)\)

   \(=\frac{2019}{1}.\left(1-\frac{1}{2019}\right)\)

   \(=\frac{2019}{1}.\frac{2018}{2019}\)

   \(=2018\)

\(A=\frac{2019}{2}+\frac{2019}{6}+\frac{2019}{12}+\frac{2019}{20}+\frac{2019}{30}+\frac{2019}{2018.2019}\)

\(A=\frac{2019}{1.2}+\frac{2019}{2.3}+\frac{2019}{3.4}+\frac{2019}{4.5}+\frac{2019}{5.6}+...+\frac{2019}{2018.2019}\)

\(A=2019.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\right)\)

\(A=2019.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2018}-\frac{1}{2019}\right)\)

\(A=2019.\left(1-\frac{1}{2019}\right)\)\(=2019.\frac{2018}{2019}=2018\)

Vậy A = 2018 

-Dấu " . " là dấu nhân.

a: \(\frac23\times\frac45+\frac23\times\frac15+\frac23\)

\(=\frac23\times\left(\frac45+\frac15\right)+\frac23\)

\(=\frac23+\frac23=\frac43\)

b: \(\frac{2022\times2023+2000}{2023\times2023-23}\)

\(=\frac{2022\times2023+2000}{2022\times2023+2023-23}\)

\(=\frac{2022\times2023+2000}{2022\times2023+2000}\)

=1

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

\(=\frac12-\frac13+\frac13-\frac14+\frac14-\frac15+\frac15-\frac16\)

\(=\frac12-\frac16\)

\(=\frac13\)

Mình tính từng bước cẩn thận nhé: \frac{1}{2} \times 3 + \frac{1}{3} \times 4 + \frac{1}{4} \times 5 + \frac{1}{5} \times 6 1. 2. 3. 4. Bây giờ cộng lại: \frac{3}{2} + \frac{4}{3} + \frac{5}{4} + \frac{6}{5} Quy đồng mẫu chung là : Cộng lại: 90 + 80 + 75 + 72 = 317 Vậy kết quả: \frac{317}{60} ≈ 5,2833…