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ko đấy. đằng này tớ chưa học . help
tinh
1-2-3-4 - ........ - 99 +100
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B= \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).....\left(1-\dfrac{1}{20}\right)\)
B= \(\dfrac{1}{2}.\dfrac{2}{3}.....\dfrac{19}{20}\)
B= \(\dfrac{1.2.....19}{2.3.....20}\)
B= \(\dfrac{1}{20}\)
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\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}\frac{3.5}{4.4}.....\frac{29.31}{30.30}=\frac{\left(1.2.3....29\right)\left(3.4.5....31\right)}{\left(2.3.4....30\right)\left(2.3.4....30\right)}=\frac{31}{30.2}=\frac{31}{60}\)
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\(A=1+2+2^2+2^3+2^4+...+2^{100}\)
\(2A=2+2^2+2^3+2^4+2^5+....+2^{101}\)
\(2A-A=\left(2+2^2+2^3+2^4+2^5+...+2^{101}\right)-\left(1+2+2^2+2^3+2^4+...+2^{100}\right)\)
\(A=2^{101}-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{101}}\)
\(\Rightarrow2A-A=1-\frac{1}{2^{101}}\)
\(\Rightarrow A=\frac{2^{101}-1}{2^{101}}\)
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a) (x+3)(x-4)-(x-1)(x+2)
=(x^2-4x+3x-12)-(x^2+2x-x-2)
=(x^2-x-12)-(x^2+x-2)
=x^2-x-12-x^2-x+2
=-2x-10=-2(x+5)
b) a^3+b^3+3a^2b+3ab^2
=(a+b)^3
1+2+22+23+24+...+22014
=2-1+22-2+23-22+24-23+25-24+...+22015-22014
=22015-1
Đăt S = 1 + 2^2 +.. + 2^2014
2S = 2 + 2^3 + ... + 2 ^2014 + 2^2015
2S - S = 2 + 2 ^3 + .. + 2^2014 + 2^2015 - 1 - 2 - 2^3 -... - 2^2014
=> S = 2^2015 - 1