`@` `\text {Ans}`

`\downarrow`

`(1/2-1/3+1/4-1/5):(1/4-1/5)`

`=`\(\left(\dfrac{1}{6}+\dfrac{1}{20}\right)\div\dfrac{1}{20}\)

`=`\(\dfrac{1}{20}\div\dfrac{1}{20}+\dfrac{1}{6}\div\dfrac{1}{20}\)

`= 1+10/3`

`= 13/3`

A = (\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)): (\(\dfrac{1}{4}\) - \(\dfrac{1}{5}\))

A = ( \(\dfrac{30}{60}\) - \(\dfrac{20}{60}\) + \(\dfrac{15}{60}\) - \(\dfrac{12}{60}\)):(\(\dfrac{5}{20}\) - \(\dfrac{4}{20}\))

A = \(\dfrac{13}{60}\): \(\dfrac{1}{20}\)

A = \(\dfrac{13}{60}\times\dfrac{20}{1}\) 

A = \(\dfrac{13}{3}\)

Sửa đề: 1/2*1/3+1/3*1/4+...+1/19*1/20

=1/2-1/3+1/3-1/4+...+1/19-1/20

=1/2-1/20=10/20-1/20=9/20

mn ơi mk lộn một xíu: 2003^{(1*9*4*6)*(1*9*4*7)*...*(1*9*9*9)} 

chứ ko phải 2003^{(19*4*6)*(1*9*4*7)*...*(1*9*9*9)} nha rất xin lỗi mấy bạn

:)))))))

\(\dfrac{1}{4}+\dfrac{x}{12}=\dfrac{8}{12}\)

\(\dfrac{3}{12}+\dfrac{x}{12}=\dfrac{8}{12}\)

\(\dfrac{3+x}{12}=\dfrac{8}{12}\)

\(\dfrac{x+3}{12}=\dfrac{8}{12}\)

\(=\)\(\dfrac{5}{12}\)

Vậy \(x=5\).

x=5 nha

tick nhó^^

Đề hơi khó hiểu bn nhé

\(\left(\dfrac{1}{4}x-\dfrac{1}{8}\right).\dfrac{3}{4}=\dfrac{1}{4}\)

\(\dfrac{1}{4}x-\dfrac{1}{8}=\dfrac{1}{4}:\dfrac{3}{4}=\dfrac{1}{3}\)

\(\dfrac{1}{4}x=\dfrac{1}{3}+\dfrac{1}{8}=\dfrac{11}{24}\)

\(x=\dfrac{11}{24}:\dfrac{1}{4}=\dfrac{11}{6}\)

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}\)

\(\text{=}\dfrac{-1}{15}+\dfrac{1}{5}+\dfrac{2}{45}\)

\(\text{=}\dfrac{8}{45}\)

Áp dụng tính chất đổi dấu và giao hoán của phép nhân phân số, ta có:

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}=\dfrac{1}{5}.\dfrac{-3}{9}+\dfrac{1}{5}.\dfrac{4}{4}+\dfrac{1}{5}.\dfrac{2}{9}\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+1+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+\dfrac{9}{9}+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}.\dfrac{8}{9}\)

                                           \(=\dfrac{8}{45}\)

=1/2+1/3+1/4+...+1/100

xét mẫu:có ssh là (100-2):1+1=99 số

tổng là (100+2)*99:2=5940

vậy ta có 1/5940

\(A=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\)

\(\Rightarrow A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(\Rightarrow A=1-\dfrac{1}{100}\)

\(\Rightarrow A=\dfrac{99}{100}\)

Đoạn suy ra đầu tiên cơ sở gì bạn suy ra được như vậy nhỉ?

\(1+4+16+...+4^{2021}\)

Đặt biểu thức trên là \(A\), ta có:

\(A=1+4+16+...+4^{2021}\)

\(A=1+4+4^{2}+...+4^{2021}\)

\(4A=4+4^{2}+4^{3}+...+4^{2022}\)

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

\(3A=4^{2022}-1\)

\(A=\dfrac{4^{2022}-1}{3}\)