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

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

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

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

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

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

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

\(S=\frac{3^8+1}{2.3^7}\)

Vậy \(S=\frac{3^8+1}{2.3^7}\)

Chúc bạn học tốt ~ 

\(1,\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\1-2x=5\end{matrix}\right.\Leftrightarrow D\\ 2,\Leftrightarrow\left(-3\right)^x=-27\cdot81=-2187=\left(-3\right)^7\\ \Leftrightarrow x=7\left(A\right)\)

1.D

2.A

1.D

2.D

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Chúc học tốt!

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

\(\Rightarrow3B=3.\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\right)\)

\(\Rightarrow3B=3+1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\)

\(\Rightarrow3B-B=\left(3+1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\right)-\)\(\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\right)\)

\(\Rightarrow2B=3-\frac{1}{2187}\)

\(\Rightarrow B=\left(3-\frac{1}{2187}\right):2\)

\(\Rightarrow B=\frac{6560}{2187}\)

Chắc sai !!!

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

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

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

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

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

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

              A     = \(\left(3-\frac{1}{3^7}\right):2\)

\(\Rightarrow1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}=\left(3-\frac{1}{3^7}\right):2\)

\(3A=1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\)

\(3A-A=\left(1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{6561}\right)\)

\(2A=\dfrac{6560}{6561}\)

\(A=\dfrac{3280}{6561}\)

Đặt \(V=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}+\dfrac{1}{2187}\)

\(\Rightarrow3V=3.\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}+\dfrac{1}{2187}\right)\)

\(\Rightarrow3V=1+\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}\right)\)

\(\Rightarrow3V=1+V-\dfrac{1}{2187}\)

\(\Rightarrow2V=1-\dfrac{1}{2187}\)

\(\Rightarrow V=\dfrac{1093}{2187}\).

1093/2187 nha bạn

A= 1/3 + 1/9 + 1/27 + 1/81 +...+1/729 + 1/2187

3A = 1 + 1/3 + 1/9 + 1/27 + 1/81 +...+1/729 

=> 3A - A = 1 - 1/2187

đề sai à

link j bạn

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