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![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1 - 2 + 22 - 23 + 24 - 25 + ...+ 2999 - 21000
2S = 2 - 22 + 23 - 24 + 25 + .... + 2998 - 2999 + 21000 - 21001
2S + S = 2 - 22 + 23 - 24 + ....+ 21000 - 21001 + 1 - 2 + 22 + ... + 2999 - 21000
3S = -21001 +1
S = \(\frac{-2^{100}+1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=3+3/2+3/22+...+3/2a nên:
=> 2A = 6+3+3/2+3/22 +...+3/2a-1
=> A= 6 - 3/2a ( lấy 2A -A )
Vậy A=6-3/2a
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1+3+32+...+3100
3A=3+32+33+...+3101
=>3A+1=1+3+32+...+3100+3101=A+3101
=>3A-A=3101-1
2A=3101-1
A=(3101-1)/2
B=1+4+42+...+450
4B=4+42+...+451
4B+1=1+4+42+...+450+451=B+451
=>4B-B=451-1
3B=451-1
B=(451-1)/3
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(2^9+2^9=2.2^9\)
\(3^4+3^4+3^4=3.3^4\)
\(A=1+2+2^2+2^3+.....+2^{2017}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+....+2^{2018}\right)-\left(1+2+2^2+2^3+....+2^{2017}\right)\)
\(\Rightarrow A=2^{2018}-1\)
\(B=1+3+3^2+....+3^{301}\)
\(\Rightarrow3B-B=\left(3+3^3+3^4+.....+3^{302}\right)-\left(1+3+3^2+....+3^{301}\right)\)
\(\Rightarrow B\left(3-1\right)=3^{302}-1\Leftrightarrow B=\frac{3^{302}-1}{3-1}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
câu nào dạng cũng giống nhau, ko biết 1 câu là ko giải đc toàn bộ
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{997.999}\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{997.999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{997}-\frac{1}{999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(1-\frac{1}{999}\right)=\frac{5}{2}.\frac{998}{999}=\frac{2495}{999}=2\frac{497}{999}\)
\(A=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}\)
\(\Leftrightarrow A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(1-\frac{1}{16}\right)=\frac{2}{3}.\frac{15}{16}=\frac{5}{8}\)
C = 5/1x3 + 5/3x5 + 5/5x7 + ... + 5/997x999
C = 5 - 5/3 + 5/3 - 5/5 + 5/5 - 5/7 + ... + 5/997 - 5/999
C = 5 - 5/999
C = bạn tự tính nhé !
A = 2/4 + 2/28 + 2/70 + 2/130 + 2/208
A = 2/1x4 + 2/4x7 + 2/7x10 + 2/10x13 + 2/13x16
A = 2 - 2/4 + 2/4 - 2/7 + 2/7 - 2/10 + 2/10 - 2/13 + 2/13 - 2/16
A = 2 - 2/16
A = bạn tự tính nhé !