Cho A=1-1/2+1/3-1/4+….+1/49-1/50 Hãy chứng tỏ 7/12 03/09/2021 Bởi Reagan Cho A=1-1/2+1/3-1/4+….+1/49-1/50 Hãy chứng tỏ 7/12 { "@context": "https://schema.org", "@type": "QAPage", "mainEntity": { "@type": "Question", "name": " Cho A=1-1/2+1/3-1/4+....+1/49-1/50 Hãy chứng tỏ 7/12
Đáp án: A= 1- 1/2+ 1/3- 1/4+ 1/5- 1/6+ … + 1/49- 1/50 =1+1/2+1/3+..+1/50-2(1/2+1/4+1/6+..+1/50) =1+1/2+1/2+..+1/50-1-1/2-..-1/25 =1/26+1/27+..+1/50 =(1/26+1/27+1/28+1/29+1/30)+(1/31+..+1/40)+(1/41+1/42+..+1/50) > (1/30+1/30+..+1/30)+(1/40+1/40+..+1/40)+(1/50+1/50+..+1/50) = 5.1/30+10.1/40+10.1/50 =37/60 > 35/60=7/12 A = 1/26+1/27+..+1/50 =(1/26+1/27+1/28+1/29+1/30)+(1/31+..+1/40)+(1/41+1/42+..+1/50) < (1/25+1/25+..+1/25)+(1/30+1/30+..+1/30)+(1/40+1/40+..+1/40) =5.1/25+10.1/30+10.1/40 =47/60 < 50/60=5/6 Giải thích các bước giải: Bình luận
Đáp án:
A= 1- 1/2+ 1/3- 1/4+ 1/5- 1/6+ … + 1/49- 1/50
=1+1/2+1/3+..+1/50-2(1/2+1/4+1/6+..+1/50)
=1+1/2+1/2+..+1/50-1-1/2-..-1/25
=1/26+1/27+..+1/50
=(1/26+1/27+1/28+1/29+1/30)+(1/31+..+1/40)+(1/41+1/42+..+1/50) >
(1/30+1/30+..+1/30)+(1/40+1/40+..+1/40)+(1/50+1/50+..+1/50)
= 5.1/30+10.1/40+10.1/50
=37/60 > 35/60=7/12
A = 1/26+1/27+..+1/50
=(1/26+1/27+1/28+1/29+1/30)+(1/31+..+1/40)+(1/41+1/42+..+1/50) <
(1/25+1/25+..+1/25)+(1/30+1/30+..+1/30)+(1/40+1/40+..+1/40)
=5.1/25+10.1/30+10.1/40
=47/60 < 50/60=5/6
Giải thích các bước giải:
Đáp án:
Giải thích các bước giải: