A = 2 - 4 - 6 + 8 + 10 - 12 - 14 + 16 + ...... + 2000 + 2002 - 2004.
A = ( 2 - 4 - 6 + 8 ) + ( 10 - 12 - 14 + 16 ) +...+ ( 1997 - 1998 - 1999 + 2000 ) + ( 2002 - 2004 )
A = 0 + 0 + ... + 0 + ( -2 )
A = -2
a) Ta có :
\(A=2-4-6+8+10-12-14+16+................+2000+2002-2004\)
\(A=\left(2-4-6+8\right)+\left(10-12-14+16\right)+.......................+\left(1997-1998-1999+2000\right)+\left(2002-2004\right)\)
\(A=0+0+......................+0+\left(-2\right)\)
\(A=-2\)
b) Ta có :
\(B=2^{2005}-2^{2004}-2^{2003}-......................-2-1\)
\(B=2^{2005}-\left(2^{2004}+2^{2003}+..................+2+1\right)\)
Đặt :
\(C=2^{2004}+2^{2003}+......................+2+1\)
\(2C=2^{2005}+2^{2004}+2^{2003}+.................+2\)
\(\Rightarrow2C-C=2^{2005}-1\)
\(\Rightarrow B=2^{2005}-C\)
\(B=2^{2005}-\left(2^{2005}-1\right)\)
\(B=2^{2005}-2^{2005}+1\)
\(B=0+1=1\)
~ Chúc bn học tốt ~
