Question

CMR 1\2²+1\3²+1\4²+....+1\100²<1

Answer 1

ta có 1/2^2+1/3^2+1/4^2+...+1/100^2<A=1/1*2+1/2*3+1/3*4+...+1/99*100

=> A= (1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)

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

       =1-1/100= 99/100 <1

=> 1/2^2+1/3^2+1/4^2+...+1/100^2<1

Answer 2

1/2^2+1/3^2+1/4^2+..+1/100^2

1/2^2<1/1.2=1-1/2

1/3^2<1/2.3=1/2-1/3

1/4^2<1/3.4=1/3-1/4

........

1/100^2<1/99.100=1/99-1/100

1/2^2+1/3^2+1/4^2+...+1/100^2<1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100

1/2^2+1/3^2+1/4^2+...+1/100^2<1-1/100=99/100<1 (đpcm)