Question

bài 6:

cho : A= 1/1²+1/2²+1/3²+1/4²+...+1/50²

CMR: A<2

Answer 1

A=1/1^2+1/2^2+1/3^2+........+1/50^2

1/1^2=1/2x2=1-1/2

1/3^2=1/3x3=1-1/3 

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

1/50^2=1/50x50=1-1/50

=>A < 1/1^2+1-1/2+1/2-1/3+1/3-1/4+.............+1/49-1/50

=>A < 1+(1-1/50)<1+1=2

=> A<2

Answer 2

A=1/1^2+1/2^2+1/3^2+........+1/50^2

1/1^2=1/2x2=1-1/2

1/3^2=1/3x3=1-1/3 

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

1/50^2=1/50x50=1-1/50

=>A < 1/1^2+1-1/2+1/2-1/3+1/3-1/4+.............+1/49-1/50

=>A < 1+(1-1/50)<1+1=2

=> A<2