\(=3^2.\frac{1}{3^5}.3^8.\frac{1}{3^3}\)

\(=9\)

Đặt A= 1/3+1/9+1/27+1/81+1/243

A= 1/3+1/3^2+1/3^3+1/3^4+1/3^5

3A=1+1/3+1/3^2+1/3^3+1/3^4

3A-A=1+1/3+1/3^2+1/3^3+1/3^4-1/3-1/3^2-1/3^3-1/3^4-1/3^5

2A=1-1/3^5

2A=242/243

A=121/243

ta bằng 121/243

duyệt nha

\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\)

\(3A-A=1-\frac{1}{3^5}\)

\(2A=1-\frac{1}{3^5}\)

\(A=\frac{1-\frac{1}{3^5}}{2}=\frac{1-\frac{1}{243}}{2}=\frac{121}{243}\)

\(A=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\\ =\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+\dfrac{1}{3^5}\\ =>3A=1+\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}\\ =>3A-A=2A=1-\dfrac{1}{3^5}\\ =>A=\dfrac{1-\dfrac{1}{3^5}}{2}=\dfrac{3^5-1}{2.3^5}\)

S = 1/3+1/9+1/27+1/81+1/243+1/729+1/2187 ( 1 ) 
Nhân S với 3. Ta có: 
S x 3 = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 ( 2 ) 
Trừ ( 2 ) với ( 1 ) ta có: 
S x 3 - S = 1 - 1/ 2187 
2S = 2186/ 2187 
S = 2186/ 2187 : 2 
S = 1093/ 2187 

Q = (1 + 2 - 3 - 4) + (5 + 6 - 7- 8) + ... + (77 + 78 - 79 - 80) - 81

Q = (-4) . 20 - 81

Q = -161

Nhân 20 vì có 80 số hạng, mỗi cặp 4 số hạng nên có 20 cặp.

ccccc

a:\(A=3^9\cdot3^8\cdot\left(-3^5\right)=-3^{22}\)

b: \(B=5^3+3^5=125+243=368\)

c: \(3C=3^{101}-3^{100}+3^{99}-...-3^2+3\)

\(\Leftrightarrow4C=3^{101}+1\)

hay \(C=\dfrac{3^{101}+1}{4}\)

\(\frac{2^{12}.243-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}\)

\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)

\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3-1\right)}\)

\(=\frac{1}{3}\)

HT

T = 5.5 + 6.6 + .... + 30.30 

T = 5.(6 - 1) + 6.(7-1) + ... + 30.(31 - 1) 

T = 5.6 - 5 + 6.7 - 6 + ... + 30.31 - 30 

T = (5.6 + 6.7 + ... + 30.31) - (5 + 6 + ... + 30) 

Đặt A = 5.6+ 6.7 + ... + 30.31  

     B = 5 + 6 + ... + 30 

Ta có : 

3A = 5.6.3 + 6.7.3 + ... + 30.31 . 3 

3A = 5.6.(7-4) + 6.7.(8-5) + ... + 30.31.(32-29) 

3A = 5.6.7 - 4.5.6 + 6.7.8 - 5.6.7 + ... + 30.31.32 - 29.30.31

3A = (5.6.7 + 6.7.8 + ... + 30.31.32) - (4.5.6 + 5.6.7 + ... + 29.30.31) 

3A  = 30.31.32 - 4.5.6 

3A = 29640

A = 29640 : 3 

A = 9880

SSH của B là : (30 - 5) : 1 + 1  = 26 (số hạng) 

Tổng B là : (30 + 5) . 26  : 2  =455 

=> T = A - B = 9880 - 455 = 9425

c, S = 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561

S = (3 + 2187) + (9 + 6561) + (27 + 243) + (81 + 729) +  1 

S = 2190 + 6570 + 270 + 810 + 1 

S = (2190 + 810) + 6570 + 270 + 1 

S = 3000 + 6570 + 270 + 1 

S = 9570 + 270 + 1 

S = 9840  + 1 

S = 9841 

Vậy S = 9841 

a, B=68×75+34×50

   B=68×75+68×25

   B=68×(75+25)

   B=68×100

   B=6800

=1/243 nha bn có j k mk nka 

\(1-\frac{2}{3}-\frac{2}{9}-\frac{2}{27}-\frac{2}{81}-\frac{2}{243}\)

\(=\frac{243}{243}-\frac{162}{243}-\frac{54}{243}-\frac{6}{243}-\frac{2}{243}=\frac{1}{243}\)