B1:Tính $lim u_{n}:$
1)  $u_{n}$= $\frac{1^2 + 2^2 +...+ n^2}{n^4 + 2n}$

2)  $u_{n}$ = $\frac{2.1^2 + 3.2^2 +...+(n+1).n^2}{n^4}$

3) $u_{n}$ = $\frac{1}{1.2.3} + \frac{1}{2.3.4} +...+ \frac{1}{n.(n+1)(.n+2)}$

4)  $u_{n}$ = $\frac{1^2 + 3^2 + ...+ (2n-1)^2}{n^3}$
2, Biển đổi tổng trên tử nha : 
$ <=> (1+1).1^2 + (2+1).2^2+...+(n+1).n^2$
$ <=> ( 1^3 + 2^3 +..+ n^3)+ ( 1^2 + 2^2+...+n^2)$
$ =\frac{n^2.(n+1)^2}{4}+\frac{n.(n+1).(2n+1)}{6}$ 
sau rút gọn tính lim như bt thôi 
tiếp đi kem –  hờ hờ 04-04-16 10:47 PM
1,
$ <=> lim\frac{n.(n+1).(2n+1)}{6.(n^4+2n)}==> lim =0 $

uk....nhưng hơi tắt đây........ –  hờ hờ 05-04-16 12:34 AM
sao kem lm đúng mà –  •♥• Kem •♥• 04-04-16 10:35 PM
3, $ \frac{-2}{3}.(\frac{1}{2.3}-\frac{1}{2.3}-\frac{1}{2.2}+\frac{1}{3.4}-\frac{1}{4.4}-\frac{1}{4.3}+...+ \frac{1}{(n+1).(n+2)}- \frac{1}{2n.(n+2)}-\frac{1}{2n.(n+1)})$

đó sau rút gọn tiếp

4,Rút gọn tổng : 

$ <=> (2.1-1)^2+ (2.2-2)^2+...+ (2n-1)^2$

$ <=> 2^2-2.2+1^2+ (2.2)^2- 2.2.2+2^2+..+ (2n)^2-4n+1^2$

$ <=> 2^2(1+2^2+..+n^2) -2.2(1+ 2+....+n)+( 1^2+2^2+n^2)$

sau áp tổng đặc biệt vào là ra tính lim như bình thường
Thanks kem –  hờ hờ 05-04-16 12:01 AM

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