Chứng minh rằng P=1/41+1/42+1/43+…+1/89>7/12 02/09/2021 Bởi Jasmine Chứng minh rằng P=1/41+1/42+1/43+…+1/89>7/12
Giải thích các bước giải: Ta có: $7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80$ $1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80$ $= (1/41 + 1/42 + 1/43 + …+ 1/60) + (1/61 + 1/62 +…+ 1/79 + 1/80)$ Do $1/41> 1/42 > 1/43 > …>1/59 > 1/60$ =>$ (1/41 + 1/42 + 1/43 + …+ 1/60) > 1/60 + …+ 1/60$ = $20/60 và 1/61> 1/62> … >1/79> 1/80$ =>$ (1/61 + 1/62 +…+ 1/79 + 1/80) > 1/80 + …+ 1/80$ = $20/80$ Vậy: $1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 20/60 + 20/80$ $= 7/12$ => $1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 7/12 $ ~ xin hay nhất ~ Bình luận
Đáp án+Giải thích các bước giải: 7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80 1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + …+ 1/60) + (1/61 + 1/62 +…+ 1/79 + 1/80) Do 1/41> 1/42 > 1/43 > …>1/59 > 1/60 => (1/41 + 1/42 + 1/43 + …+ 1/60) > 1/60 + …+ 1/60 = 20/60 và 1/61> 1/62> … >1/79> 1/80 => (1/61 + 1/62 +…+ 1/79 + 1/80) > 1/80 + …+ 1/80 = 20/80 Vậy: 1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12 => 1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 7/12 => ĐPCM Bình luận
Giải thích các bước giải:
Ta có: $7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80$
$1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80$
$= (1/41 + 1/42 + 1/43 + …+ 1/60) + (1/61 + 1/62 +…+ 1/79 + 1/80)$
Do $1/41> 1/42 > 1/43 > …>1/59 > 1/60$
=>$ (1/41 + 1/42 + 1/43 + …+ 1/60) > 1/60 + …+ 1/60$
= $20/60 và 1/61> 1/62> … >1/79> 1/80$
=>$ (1/61 + 1/62 +…+ 1/79 + 1/80) > 1/80 + …+ 1/80$
= $20/80$
Vậy: $1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 20/60 + 20/80$
$= 7/12$
=> $1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 7/12 $
~ xin hay nhất ~
Đáp án+Giải thích các bước giải:
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80 1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80
= (1/41 + 1/42 + 1/43 + …+ 1/60) + (1/61 + 1/62 +…+ 1/79 + 1/80)
Do 1/41> 1/42 > 1/43 > …>1/59 > 1/60
=> (1/41 + 1/42 + 1/43 + …+ 1/60) > 1/60 + …+ 1/60
= 20/60 và 1/61> 1/62> … >1/79> 1/80
=> (1/61 + 1/62 +…+ 1/79 + 1/80) > 1/80 + …+ 1/80 = 20/80
Vậy: 1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 20/60 + 20/80
= 7/12 => 1/41 + 1/42 + 1/43 +…+ 1/79 + 1/80 > 7/12
=> ĐPCM