Question

[Legend]

Hãy tính bằng cách hợp lí : 

1/1x2 + 1/2x3 + 1/3x4 + ... 1/9x10

Answer 1

[‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍...]

=1- 1/2 +1/2- 1/3+....+1/9- 1/10

=1- 1/10

=9/10

Answer 2

[eXistenZ XI]

1/1x2 + 1/2x3 + 1/3x4 +...+1/9x10 = 1/1 - 1/2 + 1/2 -1/3 + 1/3 -1/4 +...+1/9-1/10

=1+( 1/2 -1/2)+(1/3-1/3)+...+(1/9-1/9)-1/10

=1 + 0 + 0 +...-1/10 = 9/10