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Ta có: 3S = 3/2.5 + 3/5.8 + ... + 3/47.50
3S = 1/2 - 1/5 + 1/5 - 1/8 + ... +1/47 - 1/50
3S = 1/2 - 1/50
3S = 12/25
=> S = 12/25 : 3 = 4/25
k, đây là dạng toán sai phân hữu hạn.
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số hạng tổng quát là 1/[n.(n+3)] = (1/3).[(n+3)-n]/[n.(n+3)] = (1/3). [1/n - 1/(n+3)]
=>
A = (1/3).[(1/2 - 1/5) + (1/5 - 1/8) + (1/8 - 1/11) +...+(1/44 - 1/47) + (1/47 - 1/50)]
= (1/3).[1/2 - 1/50]
= (1/3). (24/50) = (1/3).(12/25) = 4/25
vậy A = 4/25
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good luck!
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+.......+\frac{6}{44.47}+\frac{6}{47.50}\)
\(=2\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+......+\frac{3}{44.47}+\frac{3}{47.50}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+......+\frac{1}{44}-\frac{1}{47}+\frac{1}{47}-\frac{1}{50}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{50}\right)\)
\(=1-\frac{1}{25}\)
\(=\frac{24}{25}\)
đặt \(A=\frac{1}{9.11}+\frac{1}{11.13}+........+\frac{1}{41.43}+\frac{1}{43.45}\)
\(2A=\frac{2}{9.11}+\frac{2}{11.13}+.......+\frac{2}{41.43}+\frac{2}{43.45}\)
\(2A=\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+......+\frac{1}{41}-\frac{1}{43}+\frac{1}{43}-\frac{1}{45}\)
\(2A=\frac{1}{9}-\frac{1}{45}\)
\(2A=\frac{4}{45}\)
\(A=\frac{4}{45}\div2\)
\(A=\frac{2}{45}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{5}{2.5}+\frac{5}{5.8}+\frac{5}{8.11}+...+\frac{5}{47.50}\)
\(=\frac{5}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{47.50}\right)\)
\(=\frac{5}{3}\left(\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+...+\frac{50-47}{47.50}\right)\)
\(=\frac{5}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{47}-\frac{1}{50}\right)\)
\(=\frac{5}{3}\left(\frac{1}{2}-\frac{1}{50}\right)\)
\(=\frac{4}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Q=(-1)+(-3)+(-5)+...+(-99)
Dãy số trên là dãy số cách đều -4 đơn vị và có 51 số hạng.
\(\Rightarrow\) Q = [ -99 + ( -1) . 51 : 2 = -2550
Vậy Q= -2500
S= \(\dfrac{1}{2.5}\) + \(\dfrac{1}{5.8}\) + \(\dfrac{1}{8.10}\) + ... + \(\dfrac{1}{47.50}\)
S= \(\dfrac{1}{3}\) . ( \(\dfrac{3}{2.5}\) + \(\dfrac{3}{5.8}\) + ... + \(\dfrac{3}{47.50}\) )
S= \(\dfrac{1}{3}\) . ( \(\dfrac{1}{2}\) - \(\dfrac{1}{50}\) )
S = \(\dfrac{1}{3}\) . \(\dfrac{12}{25}\)
S= \(\dfrac{4}{25}\)
Vậy S = \(\dfrac{4}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
tham khảo ở đây nha
https://olm.vn/hoi-dap/detail/222956295982.html
\(A=\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{150}-\dfrac{1}{153}\right)\)
\(=\dfrac{1}{3}.\dfrac{151}{306}=\dfrac{151}{918}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
=1/3.3(1/2.5-1/5.8-1/8.11-...-1/302.305)
=1/3.(3/2.5-3/5.8-3/8.11-...-3/302.305)
=1/3(1/2-1/5-1/5-1/8-1/8-1/11-...-1/302-1/305)
=1/3[(1/2-1/305)+(1/5-1/5)+...+(1/302-1/302)
=1/3*(1/2-1/305)=1/3*(305/610-1/610)=1/3*304/610=152/915
hình như mình làm sai hoặc sai đề , sao số lớn ghê
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2.5+1/5.8+1/8.11+...+1/29.32 (khoảng cách từ 2-5;5-8;8-11;...;29-32 là 3) suy ra
=1/3(1/2-1/5+1/5-1/8+1/8-1/11+...+1/29-1/32) (-1/5+1/5;-1/8+1/8;-1/11+1/11=0) suy ra =1/3(1/2-1/32)=1/3.15/32=5/32
1/2.5+1/5.8+1/8.9+............+1/29.32
=1/2-1/5+1/5-1/8+...............+1/29-1/32
=1/2-1/32
=15/32
ai tích mk=>mk tích lại