1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

=1/1-1/2+1/2-1/3+...-1/7

=1+(1/2-1/2+1/3-1/3+...+1/6-1/6)-1/7

=1 +0+0+...-1/7

=1-1/7

=6/7

hình như là 8/7
 

Kếết quả là 116/24

Rút gọn ra phân số tối giản là 29/6

một hình chữ nhật có chu vi 72cm chiều dài 15cm và chiều rộng 9cm thì hình chữ nhật trở thành hình vuông. Tính diện tích hình chữ nhật ban đầu

giải hộ mình nhé

mk thấy bn viết đề phải đầy đủ và chính xác

\(\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+\frac{1}{7.8}+\frac{1}{9.10}\right):\left(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)

 Đặt \(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+\frac{1}{7.8}+\frac{1}{9.10}\)

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

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

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

\(A=\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\)

\(\Rightarrow\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+\frac{1}{7.8}+\frac{1}{9.10}\right):\left(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)

\(=\left(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right):\left(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)

\(=1\)

             ~~Hok tốt~~

1/1x2+1/2x3+1/3x4+..+1/9x10

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5+...-1/10

=1-1/10

=9/10

Ta có \(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)

\(=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)\)

\(=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)

Lại có B = \(\frac{1}{51.100}+\frac{1}{52.99}+...+\frac{1}{99.52}+\frac{1}{100.51}\)

=> 151B = \(\frac{151}{51.100}+\frac{151}{52.99}+...+\frac{151}{99.52}+\frac{151}{100.51}\)

=> 151B = \(\frac{1}{51}+\frac{1}{100}+\frac{1}{52}+\frac{1}{99}+...+\frac{1}{99}+\frac{1}{52}+\frac{1}{100}+\frac{1}{51}\)

=> 151B = \(2\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{99}+\frac{1}{100}\right)\)

=> B = \(\frac{2}{151}.\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{99}+\frac{1}{100}\right)\)

Khi đó \(\frac{A}{B}=\frac{\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}}{\frac{2}{151}\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{99}+\frac{1}{100}\right)}=\frac{1}{\frac{2}{151}}=\frac{151}{2}=75,5\)

a) 1/1x5 + ... + 1/21x25

= 4 x (1-1/5 + 1/5 - 1/9 + ... + 1/21 - 1/25)

= 1/4 x (1 - 1/25)

= 1/4 x 24/25

= 6/25

A = \(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\)+...+ \(\dfrac{1}{2021\times2022}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)+...+ \(\dfrac{1}{2021}\) - \(\dfrac{1}{2022}\)

A = 1 - \(\dfrac{1}{2022}\)

A = \(\dfrac{2021}{2022}\)

\(M=\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+\frac{1}{7.8}+\frac{1}{9.10}\right)\)\(-\left(\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)

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

\(M=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{6}-\frac{1}{7}-\frac{1}{8}-\frac{1}{9}-\frac{1}{10}\)

\(M=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{2}{6}-\frac{2}{8}-\frac{2}{10}\)

\(M=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{3}-\frac{1}{4}-\frac{1}{5}\)

\(M=1-\frac{1}{2}-\frac{2}{4}\)

\(M=1-\frac{1}{2}-\frac{1}{2}\)

\(M=0\)

              HOK TỐT

1-4+7-10+....+31-34=(1-4)+(7-10)+....+(31-34)=-3+(-3)+.....+(-3) (có 12 số -3)

=-3.12=-36

tick nha

-36

-18 mà mấy người này dở à mà -36 cũng tick

21320 đúng ko

gợi ý có 5 chữ số

nhanh lên