Đáp án:a)A>B b)đpcm
Giải thích các bước giải:
a) Ta có: B=1/25+1/36+...+1/2401+1/2500=1/5²+1/6²+...+1/49²+1/50²=1/5x5+1/6x6+...=1/49x49+1/50x50
Ta có: 1/4x5>1/5x5
1/5x6>1/6x6
.........................
1/48x49>1/49x49
1/49x50>1/50x50
=> 1/4.5+1/5.6+...+1/48.49+1/49.50>1/5.5+1/6.6+...+1/49.49+1/50.50
=> A>B
b)A=1/4.5+1/5.6+...+1/48.49+1/49.50=1/4-1/5+1/5-1/6+...+1/48-1/49+1/49-1/50=1/4-1/50=23/100
3/10=30/100 23/100<30/100
=>A<3/10 mà B<A
=> B<3/10
=>đpcm