\(M=1-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\right)\)

\(=1-\left(\dfrac{3}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\right)\)

\(=1-\left(\dfrac{7}{8}+\dfrac{1}{16}+\dfrac{1}{32}\right)\)

\(=1-\left(\dfrac{15}{16}+\dfrac{1}{32}\right)\)

\(=1-\dfrac{31}{32}=\dfrac{1}{32}\)

Bài 3:

a: Ta có: \(23\left(42-x\right)=23\)

\(\Leftrightarrow42-x=1\)

hay x=41

b: Ta có: 15(x-3)=30

nên x-3=2

hay x=5

Bài 1: 

a: 32+89+68=100+89=189

b: 64+112+236=300+112=412

c: \(1350+360+650+40=2000+400=2400\)

b: A=1/3+1/9+...+1/3^10

=>3A=1+1/3+...+1/3^9

=>A*2=1-1/3^10=(3^10-1)/3^10

=>A=(3^10-1)/(2*3^10)

c: C=3/2+3/8+3/32+3/128+3/512

=>4C=6+3/2+...+3/128

=>3C=6-3/512

=>C=1023/512

d: A=1/2+...+1/256

=>2A=1+1/2+...+1/128

=>A=1-1/256=255/256

Đặt \(A=\frac54+\frac58+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

=>\(A\times2=\frac52+\frac54+\frac58+\frac{5}{16}+\frac{5}{32}\)

=>\(2\times A-A=\frac52+\frac54+\frac58+\frac{5}{16}+\frac{5}{32}-\frac54-\frac58-\frac{5}{16}-\frac{5}{32}-\frac{5}{64}\)

=>\(A=\frac52-\frac{5}{64}=\frac{160}{64}-\frac{5}{64}=\frac{155}{64}\)

Ta có: \(1+\frac54+\frac58+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

\(=1+\frac{155}{64}=\frac{64+155}{64}=\frac{219}{64}\)

1 + 5/4 + 5/8 + 5/32 + 5/64 = 37/64 = 199/ 64

Đây bạn nhé!

Đặt \(A=1+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}\)

\(=5\cdot\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)

Đặt \(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(\Rightarrow2\cdot B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow B=2\cdot B-B=1-\frac{1}{64}=\frac{63}{64}\)

\(\Rightarrow A=5\cdot\frac{63}{64}=\frac{315}{64}\)

1+80/64+40/60+20/64+10/64+5/64

1+2 27/64

3 27/64

= 2,421875 bạn nhé

219/64 nhé

\(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^{32}-1\right)\left(5^{32}+1\right)\)

\(=\frac{1}{2}\left(5^{64}-1\right)\)