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\(S=1+\frac{1}{3}+\frac{1}{3^2}+........+\frac{1}{3^n}\)
\(3S=3+1+\frac{1}{3}+.......+\frac{1}{3^{n-1}}\)
\(\Rightarrow3S-S=\left(3+1+\frac{1}{3}+......+\frac{1}{3^{n-1}}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+......+\frac{1}{3^n}\right)\)
\(\Rightarrow2S=3-\frac{1}{3^n}\Rightarrow2S=\frac{3^{n+1}-1}{3^n}\Rightarrow S=\frac{3^{n+1}-1}{2.3^n}\)
Đặt \(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)
\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}+\frac{1}{2^{2012}}\)
\(\Rightarrow2A-A=A=2-\frac{1}{2^{2012}}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^{99}}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.......+\frac{1}{2^{100}}\right)\)
\(A=1-\frac{1}{2^{100}}\)
\(A=\frac{2^{100}-1}{2^{100}}\)
\(c=\frac{3}{1^2.x^2}+\frac{5}{^{2^2.3^2}}\)+\(\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\).Rut gon C
a, A = 3/2 × 4/3 × 5/4 × ... × 81/80
A = 81/2
b) (1 - 1/2) × (1 - 1/3) × ... × (1 - 1/100)
= 1/2 × 2/3 × .. × 99/100
= 1/100
a. 60%x + 0,4x + x : 3 = 2
0.6x + 0,4x + x : 3 = 2
x(0,6 + 0,4 : 3 ) = 2
\(x.\frac{1}{3}=2=>x=2:\frac{1}{3}=\frac{1}{6}\)
câu B tự làm nha .
= ba chấm