4+9+14+19+…+499
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/4*9+1/9*14+1/14*19+...+1/1999*2004
= 1/5 (1/4 - 1/9 + 1/9 - 1/14 + ... + 1/1999 - 1/2004)
= 1/5 (1/4 - 1/2004)
= 1/5 (501/2004 - 1/2004)
= 1/5 . 125/501
= 25/501
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{4\times9}+\frac{1}{9\times14}+\frac{1}{14\times19}+...+\frac{1}{1999\times2004}\)
\(=\frac{1}{5}\times\left(\frac{5}{4\times9}+\frac{5}{9\times14}+\frac{5}{14\times19}+...+\frac{5}{1999\times2004}\right)\)
\(=\frac{1}{5}\times\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{1999}-\frac{1}{2004}\right)\)
\(=\frac{1}{5}\times\left(\frac{1}{4}-\frac{1}{2004}\right)\)
\(=\frac{1}{5}\times\frac{500}{2004}=\frac{25}{501}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
A = \(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{64.69}\)
5A = \(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{64.69}\)
5A = \(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{64}-\frac{1}{69}\)
5A = \(\frac{1}{4}-\frac{1}{69}\)
5A = \(\frac{65}{276}\)
A = \(\frac{65}{276}:5\)
A = \(\frac{13}{276}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: =1-1+5-5+7-7+8-8=0
2: =14-23+5+14-5+23+17
=28+17=45
3: =12-12+9-9+14-44-3=-33
4: =22-8-8-12+4
=22-16-8
=-2
Bài \(1\)
\(1)\) \(1-5+7-8+4-1+5-7+8\)
\(=(1-1)+(5-5)+(7-7)+(8-8)\)
\(=0+0+0+0\)
\(=0\)
\(2)\) \(14-23+(5+14)-(5-23)+17\)
\(=14-23+5+14-5+23+17\)
\(=(14+14)+(23-23)+(5-5)+17\)
\(=28+17\)
\(=45\)
\(3)\) \(12-44+9-3+14-19-9-12\)
\(=(12-12)+(9-9)+(14-44)+3\)
\(=-30+3\)
\(=-33\)
\(4)\) \(22-(4-8+12)+(-8-12+4)\)
\(=22-4+8-12-8-12+4\)
\(=22+(4+4)+(8-8)+(-12-12)\)
\(=22-24\)
\(=-2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
9/14 .<.. 11/14 4/25 .<.. 4/23 5/6 ..<. 7/8 1 ..>. 14/15
8/9 ..=. 24/27 20/19 ..>. 20/27 8/7 .>.. 9/8 1 .<..15/14
![](https://rs.olm.vn/images/avt/0.png?1311)
Số số hạng : ( 499 - 4 ) : 1 +1 = 496
Tổng : ( 499 + 4 ) x 496 : 2 = 124000
T mik nha !