1 mu 2 + 2 mu 3 + 3 mu 3 + 4 mu 3=
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\(a,A=2^1+2^2+2^3+...+2^{2019}\)
\(2A=2^2+2^3+2^4+...+2^{2020}\)
\(\Rightarrow2A-A=A=2^{2020}-2\)
\(B=1+3+3^2+3^3+...+3^{2020}\)
\(3B=3+3^2+3^3+...+3^{2021}\)
\(3B-B=2B=3^{2021}-1\)
\(B=\frac{3^{2021}-1}{2}\)
a,\(A=2^1+2^2+2^3+...+2^{2019}\)
\(2A=2^2+2^3+2^4+...+2^{2020}\)
\(2A-A=\left[2^2+2^3+2^4+...+2^{2020}\right]-\left[2^1+2^2+...+2^{2019}\right]\)
\(A=2^{2020}-2^1=2^{2020}-2\)
b, \(B=1+3+3^2+3^3+...+3^{2020}\)
\(3B=3+3^2+3^3+...+3^{2021}\)
\(3B-B=\left[3+3^2+3^3+...+3^{2021}\right]-\left[1+3+3^2+...+3^{2020}\right]\)
\(2B=3^{2021}-1\)
\(B=\frac{3^{2021}-1}{2}\)
Lần sau viết cái đề rõ rõ ra nhs!!!
a) \(A=2+2^2+2^3+................+2^{100}\)
\(\Rightarrow2A=2^2+2^3+2^4+................+2^{100}+2^{101}\)
\(\Rightarrow2A-A=\left(2^2+2^3+..............+2^{100}+2^{101}\right)-\left(2+2^2+............+2^{100}\right)\)
\(\Rightarrow A=2^{101}-2\)
b) \(B=1+3+3^2+..................+3^{2009}\)
\(\Rightarrow3B=3+3^2+3^3+..................+3^{2009}+3^{2010}\)
\(\Rightarrow3B-B=\left(3+3^2+...............+3^{2010}\right)-\left(1+3+3^2+.............+3^{2009}\right)\)
\(\Rightarrow2B=3^{2010}-1\)
\(\Rightarrow B=\dfrac{3^{2010}-1}{2}\)
c) \(C=4+4^2+4^3+................+4^n\)
\(\Rightarrow4C=4^2+4^3+.................+4^n+4^{n+1}\)
\(\Rightarrow4C-C=\left(4^2+4^3+.............+4^n+4^{n+1}\right)-\left(4+4^2+............+4^n\right)\)
\(\Rightarrow3C=4^{n+1}-4\)
\(\Rightarrow C=\dfrac{4^{n+1}-4}{3}\)
12 + 23 + 33 + 43
= 1 x1 + 2x2x2 + 3x3x3 + 4x4x4
= 1 + 8 + 27 + 64
= 100
12 + 23 + 33 + 43
= 1 + 8 + 27 + 64
= 36 + 64
= 100