tính 1+2+3+17+18+19
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{20}}{\dfrac{19}{1}+\dfrac{18}{2}+\dfrac{17}{3}+....+\dfrac{1}{19}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{20}}{1+\left(\dfrac{18}{2}+1\right)+\left(\dfrac{17}{3}+1\right)+\left(\dfrac{1}{19}+1\right)}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}}{1+\dfrac{20}{2}+\dfrac{20}{3}+...+\dfrac{20}{19}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}}{20.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{19}+\dfrac{1}{20}\right)}\)
\(=\dfrac{1}{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
* Cách làm : Tử giữ nguyên,còn mẫu ta biến đổi như sau:
Mẫu : ( \(\frac{19}{1}\)+ 1 ) + ( \(\frac{18}{2}\)+ 1 ) + ( \(\frac{17}{3}\)+ 1 ) +...+ ( \(\frac{3}{17}\)+ 1 ) + ( \(\frac{2}{18}\)+ 1 ) + ( \(\frac{1}{19}\)+ 1 ) - 19 ( vì ta cộng với 19 số 1 nên phải trừ 19 )
= \(\frac{20}{1}\)+ \(\frac{20}{2}\)+ \(\frac{20}{3}\)+...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)- 19
= \(\frac{20}{2}\)+ \(\frac{20}{3}\)+...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)+ ( \(\frac{20}{1}\)- 19)
= \(\frac{20}{2}\)+ \(\frac{20}{3}\)+ ...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)+ \(\frac{20}{20}\)
= 20.( \(\frac{1}{2}\)+ \(\frac{1}{3}\)+...+ \(\frac{1}{17}\)+ \(\frac{1}{18}\)+ \(\frac{1}{19}\)+ \(\frac{1}{20}\))
=> \(\frac{Tử}{Mâu}\)= \(\frac{1}{20}\)
Phùng Quang Thịnh biến đổi sai 1 chỗ kìa
-19 = \(\frac{20}{20}-20\)chứ mà bạn
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có phần tử \(=\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+...+\frac{18}{2}+\frac{19}{1}\)
\(=\left(\frac{1}{19}+1\right)+\left(\frac{2}{18}+1\right)+...+\left(\frac{18}{2}+1\right)+\left(\frac{19}{1}+1\right)-19\)
\(=\frac{20}{19}+\frac{20}{18}+...+\frac{20}{2}+\frac{20}{1}+\frac{20}{20}-20\)
\(=20.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{19}+\frac{1}{20}\right)\left(1\right)\)
Thay (1) vào P ta được :
\(P=\frac{20.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}}\)
\(=20\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tử số = T = \(\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+....+\frac{18}{2}+\frac{19}{1}\)
\(=\left(\frac{1}{19}+1\right)+\left(\frac{2}{18}+1\right)+\left(\frac{3}{17}+1\right)+....+\left(\frac{19}{1}+1\right)-19\)
\(=\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+....+\frac{20}{2}+20-19\)
\(=\frac{20}{2}+\frac{20}{3}+....+\frac{20}{18}+\frac{20}{19}+\frac{20}{20}\)
\(=20\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)\)
= 20.Mẫu số
\(\Rightarrow\frac{\frac{1}{19}+\frac{2}{18}+....+\frac{18}{2}+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+....+\frac{1}{19}+\frac{1}{20}}=20\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Mẫu số = 1/19 + 2/18 + 3/17 + ... + 18/2 + 19/1
= ( 1/19 + 2/18 + 3/17 + ... + 18/2 ) + ( 1 + 1 + ... + 1 )
( 18 phân số ) ( 19 số 1 )
= ( 1/19 + 1 ) + ( 2/18 + 1) + ( 3/17 +1 ) + ...+ ( 18/2 + 1 ) + 1
= 20/19 + 20/18 + 20/17 + ... + 20/2 + 20/20
= 20 x ( 1/2 + 1/3 + ... + 1/19 + 1/20 )
Vậy phân số trên= 20
Mẫu số = 1/19 + 2/18 + 3/17 + ... + 18/2 + 19/1
= ( 1/19 + 2/18 + 3/17 + ... + 18/2 ) + ( 1 + 1 + ... + 1 )
( 18 phân số ) ( 19 số 1 )
= ( 1/19 + 1 ) + ( 2/18 + 1) + ( 3/17 +1 ) + ...+ ( 18/2 + 1 ) + 1
= 20/19 + 20/18 + 20/17 + ... + 20/2 + 20/20
= 20 x ( 1/2 + 1/3 + ... + 1/19 + 1/20 )
Vậy phân số trên= 20
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có
tử số \(\frac{1}{19}+\frac{2}{18}+..+\frac{18}{2}+\frac{18}{1}=\frac{1}{19}+1+\frac{2}{18}+1+..+\frac{18}{2}+1\)
\(\frac{20}{19}+\frac{20}{18}+..+\frac{20}{2}=20\left(\frac{1}{19}+\frac{1}{18}+..+\frac{1}{2}\right)\)
Do đó ta có phân số trên bằng 20
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải chi tiết:
13 + 2 – 1 = 14 | 15 + 3 – 2 = 16 |
14 – 1 + 3 = 16 | 17 – 4 + 5 = 18 |
19 – 5 – 1 = 13 | 18 – 2 – 2 = 14 |
Lời giải :
13 + 2 - 1 = 14 15 + 3 - 2 = 16
14 - 1 + 3 = 16 17 - 4 + 5 = 18
19 - 5 - 1 = 13 18 - 2 - 2 = 14
Chúc bạn học tốt ~_~
60
= 60