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\(A=2^1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\cdot\left(2+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow2A=2^2+2^3+...+2^{11}\)
\(\Rightarrow2A-A=\left(2^2+2^3+...+2^{11}\right)-\left(2+2^2+...2^{10}\right)\)
\(\Rightarrow A=2^{11}-2\)
\(B=3^1+3^2+...+3^{100}\)
\(\Rightarrow3B=3\cdot\left(3+3^2+...+3^{100}\right)\)
\(\Rightarrow3B=3^2+3^3+...+3^{101}\)
\(\Rightarrow3B-B=\left(3^2+3^3+...+3^{101}\right)-\left(3+3^2+3^3+...+3^{100}\right)\)
\(\Rightarrow2B=3^{101}-3\)
\(\Rightarrow B=\dfrac{3^{101}-3}{2}\)
Vẽ đồ thị hàm số:
1, y = 1/4x mũ 2
2, y = -1/4 x mũ 2
3, y = -2 x mũ 2
4, y = -1/2 x mũ 2
5, y = 3 x mũ 2
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 2:
a: \(=\sqrt{\left(37-35\right)\left(37+35\right)}=\sqrt{72\cdot2}=12\)
b: \(=\sqrt{\left(65-63\right)\left(65+63\right)}=\sqrt{128\cdot2}=16\)
c: \(=\sqrt{\left(221-220\right)\left(221+220\right)}=\sqrt{441}=21\)
d: \(=\sqrt{\left(117-108\right)\left(117+108\right)}=\sqrt{225\cdot9}=3\cdot15=45\)
tra loi giup voi
NHỚ TK MK NHA BN!
Ta có:\(n^2-n=n\left(n+1\right)\Leftrightarrow n^2=n\left(n+1\right)+n\)
Áp dụng \(A=1^2+2^2+3^2+..+9^2=\left(1.0+1\right)+\left(2.1+2\right)+\left(3.2+3\right)+...+\left(9.8+9\right)\)
\(=1.2+2.3+3.4+...+8.9+1+2+3+...+9\)
Xét \(a=1.2+2.3+...+8.9\)
\(3a=1.2.3+2.3\left(4-1\right)+3.4\left(5-2\right)+...+8.9\left(10-7\right)\)
\(3a=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+7.8.9-8.9.10\)
\(3a=8.9.10\Rightarrow a=\frac{8.9.10}{3}=240\)
\(\Leftrightarrow A=240+1+2+...+9\)
\(=240+\frac{\left(1+9\right)9}{2}=240+45=285\)
Vậy A=285