cho A=1/4.5+1/5.6+…+1/48.49+1/49.49 cho B=1/25+1/36+….+1/2401+1/2500 a, so sánh A và B b,CTR B<3/10 24/10/2021 Bởi Daisy cho A=1/4.5+1/5.6+…+1/48.49+1/49.49 cho B=1/25+1/36+….+1/2401+1/2500 a, so sánh A và B b,CTR B<3/10
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=1/5×5+1/6×6+…=1/49×49+1/50×50 Ta có: 1/4×5>1/5×5 1/5×6>1/6×6 ……………………. 1/48×49>1/49×49 1/49×50>1/50×50 => 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 Bình luận
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=1/5×5+1/6×6+…=1/49×49+1/50×50
Ta có: 1/4×5>1/5×5
1/5×6>1/6×6
…………………….
1/48×49>1/49×49
1/49×50>1/50×50
=> 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