1. have lived / was built

2. arrived / had / went

3. was invented

4. to seeing

5. learning

Vì ba chàng hoàng tử là bố của hoàng tử nên chỉ có 1 người

    ba nàng công chúa là bố của nàng của chúa nên chỉ có 1 người

\(\Rightarrow\) Why were you absent from class last Monday?

Sader \(\rightarrow\) Sadder

\(A=\dfrac{-1}{3}+\dfrac{-1}{15}+\dfrac{-1}{35}+...+\dfrac{-1}{9999}\)
\(\Rightarrow-A=\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{9999}\)
\(-A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{99.101}\)

\(-2A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)

\(-2A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(-2A=1-\dfrac{1}{101}\)

\(-2A=\dfrac{100}{101}\)

\(-A=\dfrac{100}{101}:2\)

\(-A=\dfrac{50}{101}\)

\(\Rightarrow A=\dfrac{-50}{101}\)

Chúc bạn học tốt!

\(\dfrac{-x}{4}=\dfrac{-9}{x}\Rightarrow4.\left(-9\right)=x.\left(-x\right)=-36\)

\(\Rightarrow x^2=\left|-36\right|=36\)

\(\Rightarrow x=6\)

1+3+3²+3^3+...+3^11

\(=\left(1+3+3^2\right)+3^3.\left(1+3+3^2\right)+.......+3^9.\left(1+3+3^3\right)\)

\(=13+3^3.+.......+3^9.13\)

\(=13.\left(1+3^3+3^6+3^9\right)\)

ta co : \(13.\left(1+3^3+3^6+3^9\right)\) chia het cho 13

=> Achia het cho 13

b:

\(\left(1+3+3^2+3^3\right)+3^4.\left(1+3+3^2+3^3\right)+3^8.\left(1+3+3^2+3^3\right)\)

\(=40+3^4.40+3^8.40\)

\(=40.\left(3^4+3^8\right)\)

vi \(40.\left(3^4+3^8\right)\)chia het cho 40

=> A chia het cho 40

nho lik.e nha

Ngu Người uống lộn thuốc hay sao ý -_-

a) \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+...+\dfrac{1}{x.\left(x+2\right)}=\dfrac{16}{99}\)

\(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+...+\dfrac{1}{x.\left(x+2\right)}=\dfrac{16}{99}\)

\(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{\left(x+2\right)}=\dfrac{16}{99}.2\)

\(\dfrac{1}{3}-\dfrac{1}{\left(x+2\right)}=\dfrac{32}{99}\)

\(\dfrac{1}{\left(x+2\right)}=\dfrac{1}{3}-\dfrac{32}{99}\)

\(\dfrac{1}{\left(x+2\right)}=\dfrac{1}{99}\)

\(\Rightarrow x+2=99\\ x=99-2\\ x=97\)