Đề phải là \(a_n+a_{n+1}\) mới hợp lý, chứ \(a_n+a_n+1\) thì đề sai rõ ràng.

\(a_n=1+2+...+n=\dfrac{n\left(n+1\right)}{2}\)

\(a_{n+1}=1+2+...+n+\left(n+1\right)=a_n+n+1\)

\(\Rightarrow a_n+a_{n+1}=2.a_n+n+1=n\left(n+1\right)+n+1=n^2+2n+1=\left(n+1\right)^2\) (đpcm)

đợi mk tí mk lm cho

bài 1: Gọi 2 số chính phương liên tiếp là a\(^2\) và (a+1)\(^2\)( vs a\(\in\) N )

CM :S=a\(^2\) +(a+1)\(^2\)+a\(^2\).(a+1)\(^2\) là số chính phương

Thật vậy : S= a\(^2\) +(a+1)\(^2\)+a\(^2\).(a+2a+1)

                   = a\(^2\)+a\(^2\)+2a+1+a\(^4\)+2a\(^3\)+a\(^2\)

                  = (a\(^2\))\(^2\)+a\(^2\)+1\(^2\)+2.a\(^2\).a+a+2a\(^2\).1+2a.1

                  = (a\(^2\)+a+1)\(^2\) là số chính phương (đpcm)

bài 2: 

a\(_n\)=1+23+..+n =\(\frac{\left(1+n\right).n}{2}\)=\(\frac{n+n^2}{2}\)

a) a\(_n\)=1+2+3+..+n+(n+1)=\(\frac{\left(1+n+1\right).\left(n+1\right)}{2}\)

         = \(\frac{\left(n+2\right)\left(n+1\right)}{2}\)=\(\frac{n^2+n+2n+2}{2}\)=\(\frac{n^2+3n+2}{2}\)

b) S= a\(_n\)+a\(_{n+1}\)= \(\frac{n+n^2+n^2+3n+2}{2}\)

      =\(\frac{2n^2+4n+2}{2}\)=\(\frac{2\left(n^2+2n+1\right)}{2}\)

      = (n+1)\(^2\) là số chính phương

\(lim\left(u_n\right)=lim\left(\frac{n}{n^2+1}\right)=lim\left(\frac{\frac{1}{n}}{1+\frac{1}{n^2}}\right)=\frac{0}{1}=0\)

b/

\(-1\le cos\frac{\pi}{n}\le1\Rightarrow-\frac{n}{n^2+1}\le v_n\le\frac{n}{n^2+1}\)

Mà \(lim\left(-\frac{n}{n^2+1}\right)=lim\left(\frac{n}{n^2+1}\right)=0\)

\(\Rightarrow lim\left(v_n\right)=0\)

\(C^n_n+C^{n-1}_n+C^{n-2}_n=37\)

\(\Leftrightarrow1+\dfrac{n!}{\left(n-1\right)!}+\dfrac{n!}{\left(n-2\right)!2!}=37\)

\(\Leftrightarrow1+n+\dfrac{n\left(n-1\right)}{2}=37\)

\(\Rightarrow n=8\)

\(P=\left(2+5x\right)\left(1-\dfrac{x}{2}\right)^8=\left(2+5x\right).\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{x}{2}\right)^k\right)\)

\(=\left(2+5x\right).\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)\)

\(=2.\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)+5x\)\(\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)\)

\(=2.\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)+5\)\(\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^{k+1}\right)\)

Số hạng chứa \(x^3\) trong \(2.\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^k\right)\) là \(2C^3_8.\left(-\dfrac{1}{2}\right)^3x^3\)

Số hạng chứa \(x^3\) trong \(5\left(\sum\limits^8_{k=0}.C_8^k.\left(-\dfrac{1}{2}\right)^k.x^{k+1}\right)\) là \(5C^2_8.\left(-\dfrac{1}{2}\right)^2x^3\)

Vậy số hạng chứa x³ trong P là:\(\left[2.C^3_8\left(-\dfrac{1}{2}\right)^3+5C^2_8\left(-\dfrac{1}{2}\right)^2\right]x^3\)

Lần sau bạn lưu ý ghi đầy đủ yêu cầu của đề nhé.

Lời giải:

a. $A=\left\{1; 2; 3;4 5; 6; 7\right\}$

b. $B=\left\{34; 36; 38; 40\right\}$
c. $B=\left\{9; 10; 11; 12; 13\right\}$
d. $B=\left\{25; 27; 29\right\}$

Theo t/c dãy tỉ số bằng nhau :

\(\Rightarrow\frac{a_1}{a_2}=\frac{a_2}{a_3}=...=\frac{a_n}{a_{n+1}}=\frac{a_1+a_2+...+a_n}{a_2+a_3+...+a_{n+1}}\)(1)

Lại có : \(\frac{a_1}{a_2}=\frac{a_2}{a_3}=...=\frac{a_n}{a_{n+1}}=\frac{a_1}{a_2}.\frac{a_2}{a_3}....\frac{a_n}{a_{n+1}}=\frac{a_1}{a_{n+1}}\)(2)

Từ (1) và (2)

\(\RightarrowĐPCM\)

27/12/2017 lúc 18:59

Ex1: Điền từ thích hợp vào chỗ trống

 This is Ba. He(1)......... a student.Every morning he(2).........up at 5.30.He(3).............. his teeth and takes a(4)............... then has breakfast at 6.15. He goes to school(5)........six thirty.His house is(6).............his house so he walks.The classes(7)............at 7.15 and finish at 11.15.In the afternoon he plays sports with his friend,Nam. They play badminton but now they(8).................soccer.In the evening he (9)......his homework and goes to(10).........at 9.30

Ex2:Cho dạng đúng của động từ trong ngoặc

1.My sister(have)...........classes from Monday to Friday

2.She(read)................a book in her room now

3.He(get)........................up at 6.00 every day?

4.There(not be)..............a big yard behind his classroom

Dúng KG

Tại sao suy ra phần lại có?