A=1/(2x2)+1/(3x3)+...+1/(100x100) 
Nhận thấy rằng n x n -1=n x n -n+n-1=n x (n-1)+n-1=(n-1) x (n+1) 
=> A < 1/(2x2-1)+1/(3x3-1)+...+1/(100x100-1)=1/(1x3)+1/(3x5)+...+1/(99x101)=1/2-1/202<1/2<3/4

A=1/(2x2)+1/(3x3)+...+1/(100x100) Nhận thấy rằng n x n -1=n x n -n+n-1=n x (n-1)+n-1=(n-1) x (n+1) => A < 1/(2x2-1)+1/(3x3-1)+...+1/(100x100-1)=1/(1x3)+1/(3x5)+...+1/(99x101)=1/2-1/202<1/2<3/4

1 và 1/4 + 1/9 +.....+1/1000

Như vậy ta có:

1/4 + 1/9 +....+1/1000 = 1/....

Cho nên =>    1 > 1/4 +1/9 +....+1/1000

1 VÀ 1/4 + 1/9 + ..... +/1000

NHƯ VẬY TA CÓ:

1/4 + 1/9 +... +/1000 = 1/...

CHO NÊN => 1/4 + 1/9 +.... +1000

>1/4+1/4+1/16+1/16+1/16

=2/4+3/16=11/16=66/96<80/96=5/6

vậy A<5/6

A<B

ra ba\o nhyieu

A = 1/4 +1/9 + 1/16 + 1/25 + 1/36 
   =   ( 1/4 + 1/16 ) + ( 1/9 + 1/36) + 1/25
   =         5/16         +       5/36       + 1/25
   =                       65/144              + 1/25
   = 1769/3600
=> 1769/3600 < 5/6 (hay 1769/3600 < 3000/3600 -quyđồng-)
Vậy A< 5/6
Đúng nhé, tk cho mjk với-số to thiệt nhưng đúng mà-

\(\frac{5}{6}>A\)

A= 1/2²+1/3²+1/4²+1/5²+1/6²< 1/1x2+1/2x3+1/3x4+1/4x5+1/5x6

=> A < 1-1/6=5/6

\(N=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{10^2}\)

\(N>\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)

\(N>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{11}=\frac{1}{2}-\frac{1}{11}=\frac{10}{22}>\frac{9}{22}\)

Vậy N > 9/22