Lời giải:

\(A=\frac{10^{2021}+1}{10^{2020}+1}=\frac{10(10^{2020}+1)-9}{10^{2020}+1}=10-\frac{9}{10^{2020}+1}<10-\frac{9}{10^{2021}+1}=\frac{10^{2022}+1}{10^{2021}+1}=B\)

Vậy $A<B$

-3/7 + 17/26 - (2/13 - 3/7)

= -3/7 + 17/26 - 2/13 + 3/7

= (-3/7 + 3/7) + (17/26 - 2/13)

= 0 + 13/26

= 1/2

bằng 1/2 nha bạn

Cho mình hỏi là n thuộc N hay Z vậy?

soss

=9

9:3(1+2)=3(1+2)=3.3=9

Cái này là 2 đường chéo bằng nhau hay thế nào hả bạn?

bằng nhau nha bạn. mong bạn giúp mình

\(\dfrac{5}{2.7}+\dfrac{16}{7.9}-\dfrac{2}{9.11}-\dfrac{29}{11.18}\)

\(=\dfrac{5-2}{2.7}+\dfrac{7+9}{7.9}-\dfrac{11-9}{9.11}-\dfrac{11+18}{11.18}\)

\(=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{9}-\dfrac{1}{9}+\dfrac{1}{11}-\dfrac{1}{11}-\dfrac{1}{18}\)

\(=\dfrac{1}{2}-\dfrac{1}{18}=\dfrac{4}{9}\)

A = \(\dfrac{5}{2.7}\) + \(\dfrac{16}{7.9}\) - \(\dfrac{2}{9.11}\) - \(\dfrac{29}{11.18}\)

A = \(\dfrac{1}{2}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{9}\)  + \(\dfrac{1}{11}\) - \(\dfrac{1}{11}\) - \(\dfrac{1}{18}\)

A = \(\dfrac{1}{2}\) - \(\dfrac{1}{18}\)

A =  \(\dfrac{4}{9}\)

\(\dfrac{-3}{21}\) + \(\dfrac{6}{42}\) - \(\dfrac{-7}{49}\) = \(\dfrac{-1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{-1}{7}\) =  \(\dfrac{1}{7}\)

Lời giải:

\((1+\frac{1}{3})(1+\frac{1}{8})(1+\frac{1}{15})...(1+\frac{1}{99})\\ =\frac{4}{3}.\frac{9}{8}.\frac{16}{15}....\frac{100}{99}\\ =\frac{2^2.3^2.4^2....10^2}{1.3.2.4.3.5....9.11}=\frac{(2.3.4..10)(2.3.4..10)}{(1.2.3...9)(3.4.5...11)}=10.\frac{2}{11}=\frac{20}{11}\)

A = \(\dfrac{7}{18}\).[ - \(\dfrac{12}{23}\) - \(\dfrac{4}{15}\)] + \(\dfrac{7}{18}\).[\(\dfrac{8}{30}\)+ \(\dfrac{25}{23}\)]

A =- \(\dfrac{7}{18}\).\(\dfrac{12}{23}\) - \(\dfrac{7}{18}.\dfrac{4}{15}\) + \(\dfrac{7}{18}\).\(\dfrac{8}{30}\) + \(\dfrac{7}{18}\).\(\dfrac{25}{23}\)

A =  \(\dfrac{7}{18}\).(\(\dfrac{25}{23}\) - \(\dfrac{12}{23}\))  - (\(\dfrac{7}{18}\).\(\dfrac{4}{15}\) - \(\dfrac{7}{18}\).\(\dfrac{4}{15}\))

= \(\dfrac{7}{18}\).\(\dfrac{13}{23}\) - 0

= \(\dfrac{91}{414}\)

\(\dfrac{x}{25}=\dfrac{-3}{7}\cdot\dfrac{7}{6}\)

\(\Rightarrow\dfrac{x}{25}=\dfrac{-3\cdot7}{7\cdot6}\)

\(\Rightarrow\dfrac{x}{25}=\dfrac{-1}{2}\)

\(\Rightarrow x=-\dfrac{25}{2}\)