tính 1.4+4.7+7.10+...+19.22
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1: Tính tổng S
\(S=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{19.22}\)
\(4S=\dfrac{4}{1.4}+\dfrac{4}{4.7}+\dfrac{4}{7.10}+...+\dfrac{4}{19.22}\)
\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{19}-\dfrac{1}{22}\)
\(=1-\dfrac{1}{22}\)
\(S=\dfrac{21}{22}.\dfrac{1}{4}=\dfrac{21}{88}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1.
E = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{3}{7.10}\) + \(\dfrac{3}{10.13}\) + \(\dfrac{3}{13.16}\) + \(\dfrac{3}{16.19}\) + \(\dfrac{3}{19.22}\)
E = 1 - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{10}\) + ... +\(\dfrac{1}{19}\) - \(\dfrac{1}{22}\)
E = 1 - \(\dfrac{1}{22}\)
E = \(\dfrac{21}{22}\)
2.
(x - 4)(x - 5) = 0
TH1:
x - 4 = 0 => x = 4
TH2:
x - 5 = 0 => x = 5
Vậy: x = 4 hoặc x = 5
![](https://rs.olm.vn/images/avt/0.png?1311)
đề ???
Đăt A = 1.4 + 4.7 + 7.10 + ....+ 19.22
=> 9A = 1.4.9 + 4.7.9 + 7.10.9 + ...+ 19.22.9
9A = 1.4.(7+2) + 4.7.(10-1) + 7.10.(13-4) + ...+ 19.22.(25-16)
9A = 1.4.7 + 4.2 + 4.7.10 - 1.4.7 + 7.10.13 - 4.7.10 + ....+ 19.22.25 - 16.19.22
9A = 4.2 + 19.22.25
A = 1 162
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1.4+4.7+7.10+...+97.100
9A=1.4.9+4.7.9+7.10.9+...+97.100.9
=1.4(7+2)+4.7(10-1)+7.10(13-4)+...+97.100(103-94)
=8+97.100.103
=999108
\(\Rightarrow\)A=999108:9
\(\Rightarrow\)A=111012
Học tốt nha!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
Dạng này có nhiều rồi, bạn tham khảo câu hỏi tương tự cũng được
\(C=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{22}.\)
\(C=\frac{1}{1}-\frac{1}{22}\)
\(C=\frac{21}{22}\)
![](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)
`#3107.101107`
1.
a)
`1/(1*4) + 1/(4*7) + 1/(7*10) + ... + 1/(100*103)`
`= 1/3 * (3/(1*4) + 3/(4*7) + 3/(7*10) + ... + 3/(100*103) )`
`= 1/3 * (1 - 1/4 + 1/4 - 1/7 + ... + 1/100 - 1/103)`
`= 1/3* (1 - 1/103)`
`= 1/3*102/103`
`= 34/103`
b)
`-1/3 + (-1/15) + (-1/35) + (-1/63) + ... + (-1/9999)`
`= - 1/3 - 1/15 - 1/35 - 1/63 - ... - 1/9999`
`= - (1/3 + 1/15 + 1/35 + ... + 1/9999)`
`= - (1/(1*3) + 1/(3*5) + 1/(5*7) + ... + 1/99*101)`
`= - 1/2 * (2/(1*3) + 2/(3*5) + 2/(5*7) + ... + 2/99*101)`
`= - 1/2* (1 - 1/3 + 1/3 - 1/5 + ... + 1/99 - 1/101)`
`= -1/2 * (1 - 1/101)`
`= -1/2*100/101`
`= -50/101`
2.
`3/(1*4) + 3/(4*7) + ... + 3/(94*97) + 3/(97*100)`
`= 1 - 1/4 + 1/4 - 1/7 + ... + 1/94 - 1/97 + 1/97 - 1/100`
`= 1-1/100`
`= 99/100`
\(\text{Đặt: S= biểu thức cần tính}\)
\(\Rightarrow9S=1.4.7+4.7.9+......+19.22.9+4.2\)
\(\Rightarrow9S=1.4.7+4.7\left(10-1\right)+...+19.22\left(25-16\right)+8\)
\(\Rightarrow9S=19.22.25+8\Rightarrow S=1162\)
sai rồi 9S = 1.4.9 mà