Ta có \(A=\frac{10}{2^7}+\frac{10}{2^6}=\frac{5}{2^6}+\frac{10}{2^6}=\frac{15}{2^6}\)

Lại có B = \(\frac{11}{2^7}+\frac{9}{2^6}=\frac{5,5}{2^6}+\frac{9}{2^6}=\frac{14,5}{2^6}\)

Vì \(\frac{15}{2^6}>\frac{14,5}{2^6}\Rightarrow A>B\)

b) Ta có : \(A=\frac{-7}{10^{2005}}+\frac{-15}{10^{2006}}=\frac{-70}{10^{2006}}+\frac{-15}{10^{2006}}=\frac{-85}{10^{2006}}\)

Lại có B = \(\frac{-15}{10^{2005}}+\frac{-7}{10^{2006}}=\frac{-150}{10^{2006}}+\frac{-7}{10^{2006}}=\frac{-157}{10^{2006}}\)

Vì \(\frac{-85}{10^{2006}}>\frac{-157}{10^{2006}}\Rightarrow A< B\)

A=1-3+5-7+....+2001-2003+2005

A=[(1-3)+(5-7)+.....+(2001-2003)]+2005

A=[(-2)+(-2)+....+(-2)]+2005

Vì từ 1 đến 2003 có: 1002 số hạng => có 501 cặp => có 501 số -2

A=(-2) x 501 +2005

A=-1002+2005

A=1003

A=1-3+5-7+...+2001-2003+2005

A=(1-3)+(5-7)+....+(2001-2003)+2005

A=(-2)+(-2)+...+(-2)+2005

A=(-2).501+2005

A=(-1002)+2005

A=1003

B=1-2-3+4+5-6-7+8+...+1993-1994

B=(1-2-3+4)+(5-6-7+8)+....+(1989-1990-1991+1992)+(1993-1994)

B=0+0+...+0+(-1)

B=(-1)

C=1+2-3-4+5+6-7-8+9+...+2002-2003-2004+2005+2006

C=(1+2-3-4)+(5+6-7-8)+....+(2001+2002-2003-2004)+(2005+2006)

C=(-4)+(-4)+....+(-4)+4011

C=(-4).501+4011

C=(-2004)+4011

C=2007

A=1-3+5-7+...+2001-2003+2005

A= (-2) + (-2) +....+(-2)  +2005

A= -2. 501 +2005

A= -1002 +2005

A= 1003

B=1-2-3+4+5-6-7+8+...+1993-1994

B= (1-2-3+4) + (5-6-7 +8) +.......+ (1989 - 1990 -1991 +1992)+1993-1994

B= 0 + 0+....+0+ 1993-1994

B= -1

C=1+2-3-4+5+6-7-8+9+...+2002-2003-2004+2005+2006

C= (1+2-3-4) + (5+6-7-8) +.....+(2001+2002 -2003 -2004) +2005+2006

C= -4. 501 + 2005 +2006

C= -2004+2005+2006

C= 2007

\(\sqrt{2006+2\sqrt{2005}}-\sqrt{2006-2\sqrt{2005}}\)

\(=\sqrt{\left(\sqrt{2005}+1\right)^2}-\sqrt{\left(\sqrt{2005}-1\right)^2}\)

\(=\left(\sqrt{2005}+1\right)-\left(\sqrt{2005}-1\right)\)

= 2

M = \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

\(\Rightarrow\sqrt{2}M\)\(=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)

\(=\left(\sqrt{7}-1\right)-\left(\sqrt{7}+1\right)\)

= - 2

\(\Rightarrow M=-\sqrt{2}\)

\(a,\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}+\frac{3}{7}\)

\(=>\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{7}{21}+\frac{3}{7}\right)-\frac{20}{15}\)

\(=>1+\frac{16}{21}-\frac{20}{15}\)

\(=>\frac{37}{21}-\frac{20}{15}\)

\(=>\frac{3}{7}\)

\(b,12-8\cdot\left(\frac{3}{2}\right)^3\)

\(=>12-8\cdot\frac{27}{8}\)

\(=>12-27\)

\(=>-15\)

\(c,\left(\frac{1}{9}\right)^{2005}\cdot9^{2005}-96^2:24^2\)

\(=>\left(\frac{1^{2005}^{ }}{9^{2005}}\cdot9^{2005}\right)-\left(96^2:24^2\right)\)

\(=>\left(1^{2005}\right)-16\)

\(=>1-16\)

\(=>-15\)

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