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Ta có:
\(A=2+2^2+...+2^{60}\)
\(\Rightarrow2A=2^2+2^3+...+2^{61}\)
\(\Rightarrow2A-A=\left(2^2+2^3+...+2^{61}\right)-\left(2+2^2+...+2^{60}\right)\)
\(\Rightarrow A=2^{61}-2\)
Mà \(A=2^x-2\)
\(\Rightarrow2^{61}=2^x\)
\(\Rightarrow x=61\)
Vậy x = 61
\(A=2+2^2+2^3+...+2^{60}\)
\(\Rightarrow2A=\left(2.2\right)+\left(2.2^2\right)+\left(2.2^3\right)+...+\left(2.2^{60}\right)\)
\(\Rightarrow2A=2^2+2^3+2^4+...+2^{61}\)
\(\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{61}\right)-\left(2+2^2+2^3+...+2^{60}\right)\)
\(\Rightarrow A=2^{61}-2\)
Ta có :
\(A=2^x-2\)
\(\Rightarrow2^{61}-2=2^x-2\)
\(\Rightarrow2^{61}=2^x\)
\(\Rightarrow x=61\)
Vậy x = 61
1) Ta có : \(\frac{x-2}{4}=\frac{5+x}{3}\)
\(\Rightarrow\left(x-2\right).3=\left(5+x\right).4\)
\(\Rightarrow3x-6=20+4x\)
\(\Rightarrow3x=26+4x\)
\(\Rightarrow3x=26+x+3x\)
\(\Rightarrow0=26+x\)
\(\Rightarrow x=0-26\)
\(\Rightarrow x=-26\)
2) Ta có : \(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)
\(\Rightarrow\frac{1}{A}=1+2+2^2+...+2^{2012}\)
\(\Rightarrow\frac{2}{A}=2+2^2+2^3+...+2^{2013}\)
\(\Rightarrow\frac{2}{A}-\frac{1}{A}=\left(2+2^2+2^3+...+2^{2013}\right)-\left(1+2+2^2+...+2^{2012}\right)\)
\(\Rightarrow\frac{1}{A}=2^{2013}+1\)
\(\Rightarrow A=\frac{1}{2^{2013}+1}\)
\(A=5^2-\left(2^3-x\right)+4-2x\)
\(A=25-8+x+4-2x\)
\(A=21-x\)
a ) \(\frac{2.9+6.7}{8.5+4.2}\)
= \(\frac{2.9+2.3.7}{2.2.2.5+4.2}\)
= \(\frac{9+3.7}{2.5+4.2}\)= \(\frac{30}{18}\)= \(\frac{5}{3}\)
a, 2.9+6.7/8.5+4.2
=2.3.3+2.3.7/2.4.5+2.4
=2.3.(3+7)/2.4.(5+1)
=30/24
=5/4
b,297-15/1188-60
=282/1128
=1/4
c, 2^5.3^7+2^5.3^2/2^6.3^10
=2^5.(3^7+3^2)/2.2^5.3^10
=3^9/2.3.3^9
=1/6
a,x(x2-y)-x2(x+y)+y(x2-x)=x3-xy-x3-x2y+x2y-xy==-2xy
b, x(x-y)+y(x+y)=x2-xy+xy+y2=x2+y2
A = 2 + 22 + ... + 260
2A = 22 + 23 + ... + 261
2A - A = (22 + 23 + ... + 261) - (2 + 22 + ... + 260)
A = 261 - 2 = 2x - 2
=> x = 61
Vậy x = 61
\(A=2+2^2+...+2^{60}\)
\(2A=2\left(2+2^2+...+2^{60}\right)\)
\(2A=2^2+2^3+...+2^{61}\)
\(2A-A=\left(2^2+2^3+...+2^{61}\right)-\left(2+2^2+...+2^{60}\right)\)
\(A=2^{61}-2\).Ta có:
\(2^{61}-2=2^x-2\)
\(\Leftrightarrow2^{61}=2^x\Leftrightarrow x=61\)