Question

chứng minh rằng

1/2^2+1/3^2+1/4^2+.....+1/10^2<1

Answer 1

A la dat tren tong

We have: A = 1/2 ^ 2 + 1/3 ^ 2 + 1/4 ^ 2 + ........... + 1/10 ^ 2

A = 1 / 2.2 + 1 / 3.3 + 1 / 4.4 + ....... + 1 / 10:10

A  <1 / 1.2 + /2.3 + 1/3.4 +......+1/9.10

A < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ....+ 1/9 - 1/10

A < 1-1/10

Ma 1 - 1/10 = 9/10 < 1

=>A < 1 (dpcm)

Answer 2

dễ 

1/2^2=1/1.2

1/3^2=1/2.3

1/4^2=1/3.4

....

1/10^2=1/9.10

1/1.2+1/2.3+1/3.4+...+1/9.10

=(1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10)

=1-1/10

=9/10

Answer 3

dễ 

1/2^2=1/1.2

1/3^2=1/2.3

1/4^2=1/3.4

....

1/10^2=1/9.10

1/1.2+1/2.3+1/3.4+...+1/9.10

=(1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10)

=1-1/10

=9/10

Answer 4

dễ 

1/2^2=1/1.2

1/3^2=1/2.3

1/4^2=1/3.4

....

1/10^2=1/9.10

1/1.2+1/2.3+1/3.4+...+1/9.10

=(1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10)

=1-1/10

=9/10