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Phần a:
Có 100 số tự nhiên chia làm 20 nhóm từ trái sang phải mỗi nhóm năm số.
\(C=2.\left(1+2+4+8+16\right)+2^6.\left(1+2+4+8+16\right)+...+2^{96}.\left(1+2+4+8+16\right)\)
\(C=2.31+2^6.31+2^{11}.31+...+2^{96}.31\)
=> C chia hết cho 31.
Chúc em học tốt^^
\(2.C=2^2+2^3+....+2^{101}\)
\(=>2C-C=C=2^2-2^2+2^3-2^3+....+2^{100}-2^{100}+2^{101}-2\)
\(C=2^{101}-2\)
Do đó 2x-1=101
=>x=51
Chúc em học tốt^^
1)
Dễ thấy \(B=\dfrac{10^{19}}{10^{19}-3}>1\)
\(\Rightarrow B=\dfrac{10^{19}}{10^{19}-3}>\dfrac{10^{19}+2}{10^{19}-3+2}=\dfrac{10^{19}+2}{10^{19}-1}=A\)
a) \(A=\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\)
\(\Rightarrow A< \frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(\Rightarrow A< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow A< \frac{1}{2}-\frac{1}{100}< \frac{1}{2}\)
b) b = a - c => b + c = a
\(\left\{{}\begin{matrix}\frac{a}{b}\cdot\frac{a}{c}=\frac{a^2}{bc}\\\frac{a}{b}+\frac{a}{c}=\frac{ac+ab}{bc}=\frac{a\left(b+c\right)}{bc}=\frac{a^2}{bc}\end{matrix}\right.\)
\(\Rightarrow\frac{a}{b}\cdot\frac{a}{c}=\frac{a}{b}+\frac{a}{c}\)
Bước 2 bạn sai rồi. Vd: \(\frac{1}{3x3}\) đâu bằng hay nhỏ hơn \(\frac{1}{2x3}\)
a)\(C=2+2^2+2^3+....+2^{100}\)
\(=\left(2+2^2+2^3+2^4+2^5\right)+2^5\left(2+2^2+2^3+2^4+2^5\right)+...+2^{95}\left(2+2^2+2^3+2^4+2^5\right)\)
\(=62+2^5.62+...+2^{95}.62=62\left(1+2^5+...+2^{95}\right)=31.2\left(1+2^5+....+2^{95}\right)⋮31\)
\(\Rightarrow C⋮31\)
=>đccm
\(C=2+2^2+2^3+...+2^{99}+2^{100}\)
\(C=\left(2+2^2+2^3+2^4+2^5\right)+....+\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)\)
\(C=2.\left(1+2+2^2+2^3+2^4\right)+....+2^{96}.\left(1+2+2^2+2^3+2^4\right)\)
\(C=31.2+.....+2^{96}.31=31.\left(2+....+2^{96}\right)⋮31\)
Suy ra \(C⋮31\)
b) Ta có \(2.C=2^2+2^3+2^4+....+2^{99}+2^{100}+2^{101}\)
Suy ra \(2.C-C=2^{101}-2\)hay \(C=2^{101}-2\)
Khi đó \(2^{2x-1}-2=2^{101}-2\)
\(\Rightarrow2^{2x-1}=2^{101}\)
\(\Rightarrow2x-1=101\Rightarrow2x=100\Rightarrow x=50\)
Vậy x = 50
a; 3:\(\frac{2x}{5}\)= 1:0.001
3:\(\frac{2x}{5}\)=1000
\(\frac{2x}{5}\)=1000:3
\(\frac{2x}{5}\)=0.003
2x=0.003.5
2x=0.015
x=0.015:2
x=7.5
Câu c :
2\(^{2x-1}\) - 2 = C
2\(^{2x-1}\)- 2 = 2\(^{101}\)- 2
2\(^{2x-1}\)= 2\(^{101}\)
2x - 1 = 101
2x = 101 + 1 = 102
x = \(\frac{102}{2}\)= 51
Vậy x = 51
a) \(C=2+2^2+2^3+..........+2^{99}+2^{100}\)
\(C=\left(2+2^2+2^3+2^4+2^5\right)+...............+\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)\)
\(C=1.\left(2+2^2+2^3+2^4+2^5\right)+...........+2^{96}.\left(2+2^2+2^3+2^4+2^5\right)\)
\(C=1.62+............+2^{96}.62\)
Mà 62 \(⋮\)31 \(\Rightarrow C⋮31\left(đpcm\right)\)
b) \(2C=2^2+2^3+2^4+2^5+2^6+...............+2^{100}+2^{101}\)
\(2C-C=\left(2^2+2^3+2^4...........+2^{100}+2^{101}\right)-\left(2+2^2+2^3..........2^{99}+2^{100}\right)\)
\(2C-C=2^2+2^3+2^4+...........+2^{100}+2^{101}-2-2^2-2^3-.........-2^{99}-2^{100}\)
\(C=2^{101}-2^{100}\)
c) 22x-1 - 2 = C
Bạn áp dụng phần b để làm