Toán S= 1/21+1/22+1/23+1/24+………+1/150. So sanh S với 5/4 02/07/2021 By Genesis S= 1/21+1/22+1/23+1/24+………+1/150. So sanh S với 5/4
Đáp án: `S>5/4` Giải thích các bước giải: `S=1/21+1/22+1/23+…+1/149+1/150` `=>S=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/80)+…+1/150` Ta thấy `1/21>1/40;1/22>1/40;…;1/39>1/40` `=>1/21+1/22+…+1/40>1/40+1/40+…+1/40` (Có `20` số hạng) `=>1/21+1/22+…+1/40>1/2(1)` Ta thấy `1/41>1/80;1/42>1/80;…;1/79>1/80` `=>1/41+1/42+…+1/80>1/80+1/80+…+1/80` (Có `40` số hạng) `=>1/41+1/42+…+1/2(2)` Ta thấy `1/81>1/150;1/82>1/150;…;1/149>1/150` `=>1/81+1/82+…+1/150>1/150+1/150+…+1/150` (Có `70` số hạng) `=>1/81+1/82+…+1/150>7/15(3)` Từ `(1),(2)` và `(3)` ta có: `=>1/21+1/22+1/23+…+1/149+1/150>1/2+1/2+7/15` `=>1/21+1/22+1/23+…+1/149+1/150>1+7/15` `=>1/21+1/22+1/23+…+1/149+1/150>22/15>5/4` `=>1/21+1/22+1/23+…+1/149+1/150>5/4` Vậy `S>5/4`. Trả lời
Đáp án: Giải thích các bước giải: S=1/21+1/22+1/23+…+1/149+1/150 ⇒S=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/80)+…+1/150⇒S=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/80)+…+1/150 Ta thấy /1/21>1/40;122>1/40;…;1/39>1/40 1/21>1/40;1/22>1/40;…;1/39>1/40 /⇒121+1/22+…+1/40>1/40+1/40+…+1/40⇒1/21+1/22+…+1/40>1/40+1/40+…+1/40 (Có 2020 số hạng) ⇒1/21+1/22+…+1/40>1/2(1) ⇒1/21+1/22+…+1/40>1/2(1) Ta thấy 1/41>1/80;1/42>1/80;…;1/79>1/80 1/41>1/80;1/42>1/80;…;1/79>1/80 ⇒1/41+1/42+…+1/80>1/80+1/80+…+1/80⇒1/41+1/42+…+1/80>1/80+1/80+…+1/80 (Có 40 số hạng) ⇒1/41+1/42+…+1/2(2) ⇒1/41+1/42+…+1/2(2) Ta thấy 1/81>1/150;1/82>1/150;…;1/149>1150181>1150;182>1150;…;1149>1150 ⇒181+182+…+1/150>1/150+1/150+…+1/150 ⇒1/81+1/82+…+1/150>1/150+1/150+…+1/150 (Có 70 số hạng) ⇒1/81+1/82+…+1/150>7/15(3) ⇒1/81+1/82+…+1/150>7/15(3) Từ (1),(2)(1),(2) và(3) ta có: ⇒1/21+122+1/23+…+1/149+1/150>1/2+1/2+7/15 ⇒1/21+1/22+1/23+…+1/149+1/150>1/2+1/2+7/15 ⇒1/21+1/22+1/23+…+1/149+1/150>1+7/15 ⇒1/21+1/22+1/23+…+1/149+1/150>1+7/15 ⇒⇒1/21+1/22+1/23+…+1/149+1/150>22/15>5/4 ⇒1/2+1/22+1/23+…+1/149+1/150>5/4 ⇒1/21+1/22+1/23+…+1/149+1/150>5/4 Vậy S>54 No copy cô giáo mình chữa rồi Trả lời
Đáp án:
`S>5/4`
Giải thích các bước giải:
`S=1/21+1/22+1/23+…+1/149+1/150`
`=>S=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/80)+…+1/150`
Ta thấy `1/21>1/40;1/22>1/40;…;1/39>1/40`
`=>1/21+1/22+…+1/40>1/40+1/40+…+1/40` (Có `20` số hạng)
`=>1/21+1/22+…+1/40>1/2(1)`
Ta thấy `1/41>1/80;1/42>1/80;…;1/79>1/80`
`=>1/41+1/42+…+1/80>1/80+1/80+…+1/80` (Có `40` số hạng)
`=>1/41+1/42+…+1/2(2)`
Ta thấy `1/81>1/150;1/82>1/150;…;1/149>1/150`
`=>1/81+1/82+…+1/150>1/150+1/150+…+1/150` (Có `70` số hạng)
`=>1/81+1/82+…+1/150>7/15(3)`
Từ `(1),(2)` và `(3)` ta có:
`=>1/21+1/22+1/23+…+1/149+1/150>1/2+1/2+7/15`
`=>1/21+1/22+1/23+…+1/149+1/150>1+7/15`
`=>1/21+1/22+1/23+…+1/149+1/150>22/15>5/4`
`=>1/21+1/22+1/23+…+1/149+1/150>5/4`
Vậy `S>5/4`.
Đáp án:
Giải thích các bước giải:
S=1/21+1/22+1/23+…+1/149+1/150
⇒S=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/80)+…+1/150⇒S=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/80)+…+1/150
Ta thấy /1/21>1/40;122>1/40;…;1/39>1/40
1/21>1/40;1/22>1/40;…;1/39>1/40
/⇒121+1/22+…+1/40>1/40+1/40+…+1/40⇒1/21+1/22+…+1/40>1/40+1/40+…+1/40 (Có 2020 số hạng)
⇒1/21+1/22+…+1/40>1/2(1)
⇒1/21+1/22+…+1/40>1/2(1)
Ta thấy 1/41>1/80;1/42>1/80;…;1/79>1/80
1/41>1/80;1/42>1/80;…;1/79>1/80
⇒1/41+1/42+…+1/80>1/80+1/80+…+1/80⇒1/41+1/42+…+1/80>1/80+1/80+…+1/80 (Có 40 số hạng)
⇒1/41+1/42+…+1/2(2)
⇒1/41+1/42+…+1/2(2)
Ta thấy 1/81>1/150;1/82>1/150;…;1/149>1150181>1150;182>1150;…;1149>1150
⇒181+182+…+1/150>1/150+1/150+…+1/150
⇒1/81+1/82+…+1/150>1/150+1/150+…+1/150 (Có 70 số hạng)
⇒1/81+1/82+…+1/150>7/15(3)
⇒1/81+1/82+…+1/150>7/15(3)
Từ (1),(2)(1),(2) và(3) ta có:
⇒1/21+122+1/23+…+1/149+1/150>1/2+1/2+7/15
⇒1/21+1/22+1/23+…+1/149+1/150>1/2+1/2+7/15
⇒1/21+1/22+1/23+…+1/149+1/150>1+7/15
⇒1/21+1/22+1/23+…+1/149+1/150>1+7/15
⇒⇒1/21+1/22+1/23+…+1/149+1/150>22/15>5/4
⇒1/2+1/22+1/23+…+1/149+1/150>5/4
⇒1/21+1/22+1/23+…+1/149+1/150>5/4
Vậy S>54
No copy
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