Bài 1:

A = 1 + 3 + 3² + ... + 3¹⁰⁰

=> 3A = 3 + 3² + ... + 3¹⁰¹

=> 2A = 3¹⁰¹ - 1

=> A = \(\frac{3^{101}-1}{2}\)

B = 1 + 4² + 4⁴ + ... + 4¹⁰⁰

=> 8B = 4² + 4⁴ + ... + 4¹⁰²

=> 7B = 4¹⁰² - 1

=> B = \(\frac{4^{102}-1}{7}\)

Bài 2:

a) S₁ = 2² + 4² + ... + 20²

=> S₁ = 2²(1+2²+...+10²)

=> S₁ = 2².385

=> S₁ = 1540

b) S₂ = 100² + 200² + ... + 1000²

=> S₂ = 100²(1+2²+...+10²)

=> S₂ = 100².385

=> S₂ = 3850000

\(\frac{x+2}{-18}=\frac{-8}{x+2}\)

<=> (x+2)² = 144

<=> \(\left[\begin{array}{nghiempt}\left(x+2\right)^2=12^2\\\left(x+2\right)^2=\left(-12\right)^2\end{array}\right.\)

<=> \(\left[\begin{array}{nghiempt}x+2=12\\x+2=-12\end{array}\right.\)

<=> \(\left[\begin{array}{nghiempt}x=10\\x=-14\end{array}\right.\)

We have leanred English since 2013

Đặt: \(\frac{a}{b}=\frac{b}{c}=k\)

=> \(\frac{a}{b}.\frac{b}{c}=k^2\)

=> \(\frac{a}{c}=k^2\) (1)

Lại có: \(\frac{a+b}{b+c}=\frac{a}{b}=\frac{b}{c}=k\)

=> \(\left(\frac{a+b}{b+c}\right)^2=k^2\) (2)

Từ (1) và (2) => \(\left(\frac{a+b}{b+c}\right)^2=\frac{a}{c}\)

Bài 3 đề 6

Từ: \(\frac{2a}{3}=\frac{b}{4}\Rightarrow\frac{a}{\frac{3}{2}}=\frac{b}{4}\)

Áp dụng t/c dãy tỉ số bằng nhau, ta có:

\(\frac{a}{\frac{3}{2}}=\frac{b}{4}=\frac{a+b}{\frac{3}{2}+4}=\frac{11}{\frac{11}{2}}=2\)

=> \(\begin{cases}a=3\\b=8\end{cases}\)

Bài 3 đề 7:

Ta có:

2³⁰⁰ = (2³)¹⁰⁰ = 8¹⁰⁰

3²⁰⁰ = (3²)¹⁰⁰ = 9¹⁰⁰

Vì 8¹⁰⁰ < 9¹⁰⁰ nên 3²⁰⁰ > 2³⁰⁰

Còn bài trên mờ quá không thấy!

(2x-1)⁶ = 64²

<=> (2x-1)⁶ = 4⁶

<=> 2x -1 = 4

<=> 2x = 5

<=> x = \(\frac{5}{2}\)

(x+y)²=x²+y²+2xy

=>x²+y²=(x+y)²-2xy=5²-2.5

=25-10

=15

(x+y)³=x³+y³+3x²y+3xy²

(x+y)³=x³+y³+3xy(x+y)

=>x³+y³=(x+y)³-3xy(x+y)

=5³-3.5.5

=125-75=50

=>(x²+y²)(x³+y³)=x⁵+x²y³+x³y²+y⁵

(x²+y²)(x³+y³)=x⁵+y⁵+xy(x+y)

=>x⁵+y⁵=(x²+y²)(x³+y³)-xy(x+y)

=15.50-5.5=725

Bài tập 2:về thì quá khứ đơn, dùng các từ sau để hoàn thành các câu phía dưới.

teach -> taught

cook -> cooked

want -> wanted

spend -> spended

ring -> rang

be -> was

sleep -> slept

study -> studied

go -> went

write -> wrote

1.She went out with her boyfriend last night.
2. Laura cooked a meal yesterday afternoon.
3. Mozart wrote more than 600 pieces of music.
4. I was tired when I came home.
5. The bed was very comfortable so they slept very well.
6. Jamie passed the exam because he studied very hard.
7. My father taught the teenagers to drive when he was alive.
8. Dave wanted to make a fire but there was no wood.
9. The little boy spended hours in his room making his toys.
10. The telephone rang several times and then stopped before I could answer it.