Question

CMR 1/2x2+1/4x4+1/6x6+........=1/100x100<1/2

Answer 1

bn giở sách phát triển nâng cao ra là có mà

Answer 2

ta đặt vế trái là A ta có:

A=1/2.2 .(1+1/2.2+1/3.3+1/4.4+...+1/50.50)

A< 1/2.2.(1+1/1.2+1/2.3+1/3.4+1/4.5+...+1/49.50)

A< 1/2.2.(1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....+1/49-1/50)

A< 1/2.2.(1+1-150)

A< 1/2.2.99/50

A< 1/4.99/50

A< 99/200<100/200=1/2

=>A<1/2