62+64+66+...+698+6100
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C = 1 + 6 + 62+ 63+...+ 6100
6C = 6 + 62+ 63 +...+ 6100 + 6101
6C - C = 6101 - 1
5C = 6101 - 1
C = \(\dfrac{6^{101}-1}{5}\)
\(C=1+6+6^2+...+6^{100}\)
\(\Rightarrow C=\dfrac{6^{100+1}-1}{6-1}\)
\(\Rightarrow C=\dfrac{6^{101}-1}{5}\)
1.telling
2.to see
3.taking
4.to smoke
5.to go
6.interrupting
7.having
8.to say
9.to go
10.being
- telling → He delayed telling her the news, waiting for the right moment.
- to see → I demand to see the manager.
- to take → My father offered to take us to the airport.
- smoking → I haven't missed smoking like I expected to.
- going → We've had to postpone going to France because the children are ill.
- to interrupt → I hate to interrupt, but it's time we left.
- having → She admitted to having stolen the car.
- to say → Katie chose to say away from work that day.
- to go → Hurry up! We're waiting to go.
- being → I don't appreciate being treated like a second-class citizen.
📌 Đáp án nhanh
1. telling
2. to see
3. to take
4. smoking
5. going
6. to interrupt
7. having
8. to say
9. to go
10. being
16-18+20-22+24-26+28-....-62+64-66+68
= 16 +(20-18) + (24-22) + ( 28-26 ) +........+ (68-66)
= 16 +2+2+2+.....+2
= 16 + 2.26
= 68
các phép tính trong ngoặc đều bằng 0
suy ra chỉ còn 2005 +69 = 2074
đâu phải chọn abc j đâu. mấy cái này là câu hỏi hết mà=/
Vì \(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}<\frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)
\(\frac{1}{61}+\frac{1}{62}+...+\frac{1}{66}<\frac{1}{60}+\frac{1}{60}+...+\frac{1}{60}=\frac{6}{60}=\frac{1}{10}\)
=> A < \(\frac{1}{3}+\frac{1}{4}+\frac{1}{10}=\frac{41}{60}<\frac{45}{60}=\frac{3}{4}\)điều phải c/m
Đặt \(A=6^2+6^4+6^6+...+6^{98}+6^{100}\)
Ta có: \(A=6^2+6^4+6^6+...+6^{98}+6^{100}\)
\(\Leftrightarrow36A=6^4+6^6+...6^{100}+6^{102}\)
\(\Leftrightarrow A-36A=6^2+6^4+6^6+...6^{98}+6^{100}-6^4-6^6-...-6^{100}-6^{102}\)
\(\Leftrightarrow-35\cdot A=6^2-6^{102}\)
\(\Leftrightarrow A=\dfrac{6^{102}-6^2}{35}\)