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S = 1 + 1/3 + 1/9 + 1/27 +.....+ 1/2187

S x 3 = 3 + 1 + 1/3 + 1/9 + 1/27 +........+ 1/729

S x 3 - S = ( 3 + 1 + 1/3 + 1/9 + 1/27 +........+ 1/729 ) - ( 1 + 1/3 + 1/9 + 1/27 +.....+ 1/2187 )

S x 3 - S = 3 - 1/2187

S x 3 - S = 6560/2187

S = 6560/2187 : 2

Vậy S = 6560/4374

S x 3 = 3 + 1 + 1/3 + 1/9 + 1/27 + ..................... + 1/729

S x 3 – S = 3 – 1/2187 = 6560/2187

Vậy S =  6560/2187 : 2 = 6560/4374

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

\(3S=3+1+\frac{1}{3}+...+\frac{1}{3^6}\)

\(3S-S=\left(3+1+\frac{1}{3}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)

\(2S=3-\frac{1}{3^7}\)

\(S=\frac{3-\frac{1}{3^7}}{2}\)

S= 1+ \(\frac{1}{3}\)+ \(\frac{1}{9}\)+...+ \(\frac{1}{729}\)+ \(\frac{1}{2187}\).

=> S= 1+ \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+...+ \(\frac{1}{3^6}\)+ \(\frac{1}{3^7}\).

=>3S= 3+ 1+ \(\frac{1}{3}\)+...+ \(\frac{1}{3^5}\)+ \(\frac{1}{3^6}\).

=> 3S- S=( 3+ 1+ \(\frac{1}{3}\)+...+ \(\frac{1}{3^5}\)+ \(\frac{1}{3^6}\))-( 1+ \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+...+ \(\frac{1}{3^6}\)+ \(\frac{1}{3^7}\)).

=> 2S= 3- \(\frac{1}{3^7}\).

=> 2S= 3- \(\frac{1}{2187}\).

=> 2S= \(\frac{6560}{2187}\).

=> S= \(\frac{6560}{2187}\): 2.

=> S= \(\frac{3280}{2187}\).

Vậy S= \(\frac{3280}{2187}\).

\(S=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)

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

\(\Rightarrow\)\(3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)

\(\Rightarrow\)\(3S-S=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)

\(\Rightarrow\)\(2S=1-\frac{1}{3^7}\)

\(\Rightarrow\)\(S=\frac{1-\frac{1}{3^7}}{2}\)

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

\(3S=1+\frac{1}{3}+...+\frac{1}{3^6}\)

\(3S-S=\left(1+\frac{1}{3}+...+\frac{1}{3^6}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)

\(2S=1-\frac{1}{3^7}\)

\(S=\frac{1-\frac{1}{3^7}}{2}\)

\(S=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)

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

\(\Rightarrow3S=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)

\(\Rightarrow3S-S=1-\frac{1}{3^7}\)

\(2S=1-\frac{1}{3^7}\)

\(\Rightarrow S=\frac{1-\frac{1}{3^7}}{2}\)

P = 78 × 31 + 78 × 24 + 78 × 17 + 22 × 72

P = 78 × (31 + 24 + 17) + 22 × 72

P = 78 × 72 + 22 × 72

P = 72 × (78 + 22)

P = 72 × 100

P = 7200

S = 1 + 1/3 + 1/9 + 1/27 + ... + 1/2187

3S = 3 + 1 + 1/3 + 1/9 + ... + 1/729

3S - S = (3 + 1 + 1/3 + 1/9 + ... + 1/729) - (1 + 1/3 + 1/9 + 1/27 + ... + 1/2187)

2S = 3 - 1/2187

2S = 6560/2187

S = 6560/2187 : 2

S = 6560/2187 × 1/2

S = 3280/2187

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