\(A=47.36+64.47+15\)

\(A=47.\left(36+64\right)+15\)

\(A=47.100+15\)

\(A=4700+15\)

\(A=4715\)

\(B=27+35+65+73+75\)

\(B=\left(27+73\right)+\left(35+65\right)+75\)

\(B=100+100+75\)

\(B=275\)

\(C=37+37.15+84.37\)

\(C=37.\left(1+15+84\right)\)

\(C=37.100\)

\(C=3700\)

\(D=\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+\frac{1}{23.24}\)

\(D=\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+\frac{1}{23}-\frac{1}{24}\)

\(D=\frac{1}{20}-\frac{1}{24}\)

\(D=\frac{24}{480}-\frac{20}{480}\)

\(D=\frac{4}{480}=\frac{1}{120}\)

\(E=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(E=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(E=1-\frac{1}{50}\)

\(E=\frac{49}{50}\)

A = 47 x 36 + 64 x 47 + 15

A= 47 x ( 64 + 36 ) + 15 = 47 x 100 + 15 = 4700 + 15 = 4715

vậy A= 4715

B= 27+35 + 65 + 73+ 75

B= (27+ 73) + ( 35 + 65) +75

B= 100 +100 +75 = 275

vậy B= 275

C= 37 +37 x 15 +37 x 84 

C= 37 x ( 1+15 +84 )= 37 x 100 = 3700

 vậy C= 3700

D = 1/20x21  +  1/21x22    +    1/22x23    +    1/23x24

D= 1/20   -   1/21   +    1/21  -  1/22   + 1/22   -   1/23  +   1/23   -    1/24

D= 1/20 -1/24 = 1/120 vậy D= 1/120

E= 1/1x2   +  1/2x3 + ...... + 1/49x50

E= 1/1  -   1/2    +    1/2  -   1/3  +...... + 1/49   -   1/50

E = 1 - 1/50 = 49/50 

vậy E= 49/50

 CHÚC HOK TOT

khó quá

a) \(A=1+2+2^2+...+2^{80}\)

\(2A=2+2^2+2^3+...+2^{81}\)

\(2A-A=2+2^2+2^3+...+2^{81}-1-2-2^2-...-2^{80}\)

\(A=2^{81}-1\)

Nên A + 1 là:

\(A+1=2^{81}-1+1=2^{81}\)

b) \(B=1+3+3^2+...+3^{99}\)

\(3B=3+3^2+3^3+...+3^{100}\)

\(3B-B=3+3^2+3^3+...+3^{100}-1-3-3^2-...-3^{99}\)

\(2B=3^{100}-1\)

Nên 2B + 1 là:

\(2B+1=3^{100}-1+1=3^{100}\)

2) 

a) \(2^x\cdot\left(1+2+2^2+...+2^{2015}\right)+1=2^{2016}\)

Gọi:

\(A=1+2+2^2+...+2^{2015}\)

\(2A=2+2^2+2^3+...+2^{2016}\)

\(A=2^{2016}-1\)

Ta có:

\(2^x\cdot\left(2^{2016}-1\right)+1=2^{2016}\)

\(\Rightarrow2^x\cdot\left(2^{2016}-1\right)=2^{2016}-1\)

\(\Rightarrow2^x=\dfrac{2^{2016}-1}{2^{2016}-1}=1\)

\(\Rightarrow2^x=2^0\)

\(\Rightarrow x=0\)

b) \(8^x-1=1+2+2^2+...+2^{2015}\)

Gọi: \(B=1+2+2^2+...+2^{2015}\)

\(2B=2+2^2+2^3+...+2^{2016}\)

\(B=2^{2016}-1\)

Ta có:

\(8^x-1=2^{2016}-1\)

\(\Rightarrow\left(2^3\right)^x-1=2^{2016}-1\)

\(\Rightarrow2^{3x}-1=2^{2016}-1\)

\(\Rightarrow2^{3x}=2^{2016}\)

\(\Rightarrow3x=2016\)

\(\Rightarrow x=\dfrac{2016}{3}\)

\(\Rightarrow x=672\)

a, 2.(x – 5)+7 = 77

<=> 2.(x – 5) = 70 <=> x – 5 = 35 <=> x = 40

b,  x - 1 3 - 3 5 : 3 4 + 2 . 2 3 = 14

<=> x - 1 3 - 3 + 2 4 = 14

<=>  x - 1 3 = 14 + 3 - 16 = 1

<=> x – 1 = 1 <=> x = 2

c,  1 + 2 + 2 2 + 2 3 + . . . + 2 2016 = 2 x - 1 - 1

Đặt: A = 1 + 2 + 2 2 + 2 3 + . . . + 2 2016 => 2A =  2 + 2 2 + 2 3 + . . . + 2 2017

=> 2A – A = ( 2 + 2 2 + 2 3 + . . . + 2 2017 ) – ( 1 + 2 + 2 2 + 2 3 + . . . + 2 2016 )

=> A =  2 2017 - 1

Ta có:  1 + 2 + 2 2 + 2 3 + . . . + 2 2016 = 2 x - 1 - 1 =>  2 2017 - 1 =  2 x - 1 - 1 => x = 2018

d,  5 2 x - 3 - 2 . 5 2 = 5 2 . 3

<=>  5 2 x - 3 = 5 2 . 3 + 5 2 . 2

<=>  5 2 x - 3 = 5 2 . ( 3 + 2 )

<=>  5 2 x - 3 = 5 3

<=> 2x – 3 = 3 => x = 3

a)\(\frac{7}{1}.\frac{5}{9}.\frac{11}{35}=\frac{7.5.11}{9.5.7}=\frac{11}{9}\)

b) \(\frac{3}{5}.\frac{4}{23}.\frac{5}{6}=\frac{3.2.2.5}{5.23.3.2}=\frac{2}{23}\)

c) \(\frac{5}{2}.\frac{7}{4}.\frac{2}{7}=\frac{5.7.2}{2.7.4}=\frac{5}{4}\)

d)  \(\frac{19}{23}.\frac{12}{17}.\frac{85}{24}=\frac{19.12.5.17}{23.17.12.2}=\frac{19.5}{23.2}=\frac{95}{46}\)

Tính

A. \(\frac{7}{1}x\frac{5}{9}x\frac{11}{35}=\frac{7x5x11}{1x9x35}=\frac{11}{9}\)

B. \(\frac{3}{5}x\frac{4}{23}x\frac{5}{6}=\frac{3x4x5}{5x23x6}=\frac{2}{23}\)

C. \(\frac{5}{2}x\frac{7}{4}x\frac{2}{7}=\frac{5x7x2}{2x4x7}=\frac{35}{28}\)

D. \(\frac{19}{23}x\frac{12}{17}x\frac{85}{24}=\frac{19x12x85}{23x17x24}=\frac{4845}{2346}\)