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Gọi d là ƯCLN(2n+5,n+3)(d\(\in\)N*)

Ta có:\(2n+5⋮d,n+3⋮d\)

\(\Rightarrow2n+5⋮d,2\cdot\left(n+3\right)⋮d\)

\(\Rightarrow2n+5⋮d,2n+6⋮d\)

\(\Rightarrow\left(2n+6\right)-\left(2n+5\right)⋮d\)

\(\Rightarrow1⋮d\Rightarrow d=1\)

Vì ƯCLN(2n+5,n+3)=1

\(\Rightarrow\frac{2n+5}{n+3}\) là phân số tối giản

Gọi d là ƯCLN(2n+5,n+3)(d

N*)

Ta có:2n+5⋮d,n+3⋮d

⇒2n+5⋮d,2⋅(n+3)⋮d

⇒2n+5⋮d,2n+6⋮d

⇒(2n+6)−(2n+5)⋮d

⇒1⋮d⇒d=1

Vì ƯCLN(2n+5,n+3)=1

I.Choose the word whose underlined is pronounced differently from that of the rest.

1.    A. chore                              B. match                             C. chemical                         D. armchair

2.    A. mend                              B. semester                        C. letter                                D. report

3.    A. match                             B. pan                                 C. transmit                           D. safety

4.    A. knife                               B. socket                            C. desk                                 D. bookshelf

5.    A. head                               B. reading                          C. ready                               D. measure

II.Choose the word (A, B, C or D) that best completes the sentence.

1.    A: Can you help me carry my bags, please? B: -_________.

            A. Certainly                   B. Yes, I can                      C. Yes, please                     D. No, thanks

2.    I used to _________book before going to bed.

            A. read                           B. reading                          C. reads                                D. to read

 3.   Nam is not _________to be in my class.

            A. very old                    B. old enough                    C. too old                             D. enough old

4.    I’ll come and pick you up _________6:30 this evening, is it O.K?

            A. in                                B. at                                    C. on                                     D. to

5.    He is not _________to get married.

            A. enough old               B. enough young              C. old enough                      D. young enough

6.    Alexander Graham Bell was born_________3^rd March, 1847.

            A. in                                B. on                                   C. at                                      D. during

7.    Would you like _________a message?

            A. to leave                     B. leave                              C. leaving                            D. left

8.    We must be there _________7.30 and 10.30.

            A. at                                B. before                            C. between                           D. after

9.    My father used _________us to the zoo when we were young.

            A. took                           B. taking                            C. to take                             D. take                  

 10.   Nam hates _________home alone.

            A. to live                        B. lives                               C. live                                   D. living

11.   My mother is _________tired _________cook tonight.

            A. enough/to                 B. too/ to                            C. so/ that                            D. very/ to

12.   She has _________over 30 pages since yesterday.

            A. writen                        B. wrote                             C. written                             D. write

13.   London is _________capital city in Europe.

            A. larger                         B. the largest                     C. most large                       D. large

14.   At the end of the film “Romeo and Juliet”, they killed _________.

            A. herself                       B. himself                          C. themselves                      D. ourselves

15.   Vietnamese is different _________English.          

            A. from                           B. as                                    C. like                                   D. with

III.Choose the words or phrases that needs correction.

1.     They (have lived) (in the country) (since) (ten years).

                       A                 B               C         D

2.      We (enjoy) (to go) (for a walk) (in the morning).

                  A        B          C                D

3.        Hoa (usually) (visits us) (in) (Sunday).

                     A         B         C     D

4.        Nam (must)(helps his mother) (do) (the housework).

                    A      B                                       C           D

5.        Airmail is (very) (expensive) (than) (surface mail).

                            A                 B             C          D

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

A=\(\frac{1}{2\cdot2}+\frac{1}{3\cdot3}+\frac{1}{4\cdot4}+...+\frac{1}{100\cdot100}\)

A<\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

A<\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

A<\(1-\frac{1}{100}=\frac{99}{100}< 1\)

Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\)

Ta có : \(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};\frac{1}{4^2}< \frac{1}{3.4};...;\frac{1}{100^2}< \frac{1}{99.100}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

Đặt : \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

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

\(\Rightarrow A=\frac{1}{1}-\frac{1}{100}=\frac{99}{100}\)

Vì : \(A< 1\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\)

Vậy ...

Ta có :

\(\begin{cases}\frac{1}{2^2}< \frac{1}{1.2}\\\frac{1}{3^2}< \frac{1}{2.3}\\.....\\\frac{1}{100^2}< \frac{1}{99.100}\end{cases}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{100^2}< \frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\)

Mà \(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}< 1\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{100^2}< 1\)

Ta có: \(\frac{1}{2^2}< \frac{1}{1.2}\)

\(\frac{1}{3^2}< \frac{1}{2.3}\)

\(\frac{1}{4^2}< \frac{1}{3.4}\)

..........................

\(\frac{1}{100^2}=\frac{1}{99.100}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

Vì \(1-\frac{1}{100}< 1\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\)

Tớ làm giống như Silver bullet

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