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

CMR: A ko là số tự nhiên

CMR:

a) \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}< \frac{1}{2}\)

b) \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}< 1\)

CMR:

a) \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)

b) Cho A = \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

CMR: \(\frac{7}{12}< A< \frac{5}{6}\)

CMR:

a) \(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)

b) \(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+\frac{3.4-1}{4!}+...+\frac{99.100-1}{100!}< 2\)

a)\(\left(\frac{2}{3}+\frac{4}{5}+\frac{12}{7}\right)+\left(2^7.5^6-\frac{25^3}{\left(0.125\right)3}\right).\left(0.0001\right)^2\)

b) \(2\frac{1}{315}.\frac{1}{651}-\frac{1}{105}.3\frac{650}{651}-\frac{4}{315.651}+\frac{4}{105}\)

a)\(1-\frac{1}{3}-\frac{1}{6}-\frac{1}{10}-\frac{1}{15}-...-\frac{1}{45}\)

Combine the pairs of sentences using "so,too,either neither".

1.They can play volleyball. We can play volleyball.

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2.Mr.Tam won't come to the party tonight. His wife won't come to the party tonight.

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3.My father didn't drink beer. My uncle didn't drink beer.

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4.She is learning Enghlish. I am learning English.

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5.I'm not a doctor. They aren't doctors.

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6.They mustn't stay up late. You mustn't stay up late

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7.He got up late. I got up late.

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8.They drank milk. We drank milk.

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9.She played tennis. He played tennis

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10.I watch TV. He watched TV.

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11.I am tired. She is tired.

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12.We buy some bananas. He buys some bananas.

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13.She doesn't like beef. I don't like beef.

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14.They can't speak English. He can't speak English

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15.We didn't live in the city. They didn't live in the city

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16.He loves roses. I love roses

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17.I won't go the the zoo. They won't go to the zoo.

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Use "too, so, either, neither" to write the sentences with the words in the brackets:

1.Lien doesn't like beef. (I)

2.I ate milk and bread for breakfast this morning. (my brother)

3.Mrs.Oanh is going to the market. (we)

4.She won't buy any eggs. (they)

5.Minh wasn't at home last night. (his parents)

6.Hoa can cook very well (her sister)

7.I didn't wash the spinach (Ba)

8.Nga hates peas and carrots. (her aunt)

9.These pineapples aren't ripe (these bananas)

10.Mr.Hoang prefers ice-cream. (his children)

REWRITE:

1.Cars cause poluttion but people still want them

->Although............................................................

2.Although his leg was broken ,he managed to get out of the car

->In spite.......................................................................................

3.The café was crowded ,but we found a table

->Although..........................................................

4.She was seriously ill but she enjoyed life very much

->Although........................................................................

5.He crashed his car although he drove carefully

->Despite........................................................................

6.Although the weather was very hot , they continued playing football

->In spite of.....................................................................................

7.They got wet to the skin because of heavy rain

->It rained......................................................................

8.Our guests arrived late because of the heavy rain

->Because...........................................................

9.Because of my friends's absence, I have to copy the lesson for him

->Because..................................................................................

10.This boy isignorant because he is lazy

->Because of................................................

11.My friend was absent because of his illness

->Because.........................................................

12.Since he was careless, Tim lost his job

->Because of..................................................