Question

chứng tỏ

1/2^2+1/3^2+1/2002^2+1/2003^2<1

Answer 1

ta có 1/2^2<1/1.2;1/3^2<1/2.3;...;1/2002^2<2001.2002;1/2003^2<1/2002.2003

suy ra 1/1.2+1/2.3+...+1/2001.2002+1/2002.2003

= 1-2/2+1/2-1/3+...+1/2001-1/2002+1/2002-1/2003

=1-1/2003

mà 1/2^2+1/3^2+...+1/2002^2+1/2003^2<1-1/2003<1

Answer 2

Ta có:

1/2² = 1/1.2

1/3² < 1/2.3

1/2002² < 1/2001.2002

1/2003² < 1/2002.2003

Suy ra : 1/2² + 1/3² + 1/2002² + 1/2003² < 1/1.2 + 1/2.3 + 1/2001.2002 + 1/2002.2003

1/2² + 1/3² + 1/2002² + 1/2003² < (1 - 1/2 + 1/2 -1/3 )+(1/2001 - 1/2002 + 1/2002 -1/2003)

1/2² + 1/3² + 1/2002² + 1/2003² <  2/3 +1/2002 -1/2003<1

1/2² + 1/3² + 1/2002² + 1/2003² < 1

Answer 3

sao lại1/2^2=1/1.2