Question

Tính tổng: S=1/3+1/3^2+1/3^3+...+1/3^8+1/3^9

Answer 1

\(S=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^9}\)

\(S\cdot\frac{1}{3}=\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{10}}\)

\(S\cdot\frac{-2}{3}=\frac{1}{3^{10}}-\frac{1}{3}\)

\(S=\frac{\frac{1}{3^{10}}-\frac{1}{3}}{-\frac{2}{3}}\)

Answer 2

S=1/3+1/3^2+1/3^3+...+1/3^8+1/3^9

1/3S=1/3^2+1/3^3+1/3^4+...+1/3^9+1/3^10

S-1/3S=(1/3+1/3^2+1/3^+...+1/3^8+1/3^9)-(1/3^2+1/3^3+1/3^4+...+1/3^9+1/3^10)

2/3S=1/3-1/3^10

S=(1/3-1/3^10):2/3

Answer 3

Ta có:3S=1+1/3+1/3^2+...+1/3^7+1/3^8

3S-S=(1+1/3+1/3^2+...+1/3^7+1/3^8)-(1/3+1/3^2+1/3^3+...+1/3^8+1/3^9)

2S=1-1/3^9

2S=19682/19683

S=9841/19683

Answer 4

S=1/3+1/3^2+1/3^3+...+1/3^8+1/3^9

S=1/3+1/9+1/27+...+1/6561+1/19683

S*3=(1/3+1/9+1/27+...+1/6561+1/19683)*3

S*3=1+1/3+1/9+1/27+...+1/6561

S*3-S=1+1/3+1/9+1/27+...+1/6561-1/3-1/9-1/27-...-1/6561-1/19683

S*2=1-1/19683

S*2=19682/19683

S=19682/19683:2

S=9841/19683

Answer 5

\(S=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}+\frac{1}{3^9}\)

\(3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}+\frac{1}{3^8}\)

\(3S-S=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}+\frac{1}{3^8}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}+\frac{1}{3^9}\right)\)

\(2S=1-\frac{1}{3^9}\)

\(\Rightarrow S=\frac{1-\frac{1}{3^9}}{2}\)

Answer 6

S=1/3+1/3^2+1/3^3+...+1/3^8+1/3^9

S=1/3+1/9+1/27+...+1/6561+1/19683

S*3=(1/3+1/9+1/27+...+1/6561+1/19683)*3

S*3=1+1/3+1/9+1/27+...+1/6561

S*3-S=1+1/3+1/9+1/27+...+1/6561-1/3-1/9-1/27-...-1/6561-1/19683

S*2=1-1/19683

S*2=19682/19683

S=19682/19683:2

S=9841/19683

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