Question

chứng minh rằng : A =  1/3² +1/4²+1/5²+...+1/100² < 1/2

Answer 1

\(\frac{1}{3^2}

Answer 2

ta thấy:

1/3^2<1/2.3

1/4^2<1/3.4

.................

1/100^2<1/99.100

=>1/3^2+1/4^2+1/5^2+.........1/100^2<1/2.3+1/3.4+1/4.5+....+1/99.100

=1/2-1/3+1/3-1/4+.........+1/99-1/100

=1/2-1/100<1/2(đpcm)

 

Answer 3

chứng minh rằng : A =  1/3² +1/4²+1/5²+...+1/100² < 1/2