Ta có :
S = 30 + 32 + 34 + 36 + ....... + 32002 ( 1 )
9S = 32 + 34 + 36 + ....... + 32004 ( 2 )
Lấy ( 1 ) - ( 2 ) ta có
9S - S = ( 32 + 34 + 36 + ....... + 32004 ) - ( 30 + 32 + 34 + 36 + ....... + 32002 )
8S = 32004 - 30 = 32004 - 1
S = \(\frac{3^{2004}-1}{8}\)
Nhân S với 32 ta có :
9S = 32 + 34 + ... + 32002 + 32004
9S - S = ( 32 + 34 + ... + 32004 ) - ( 32 + 34 +... + 32002)
8S = 32004-3 = 3 ( 32003 - 1 )
=> 8S = \(\frac{3}{8}\). ( 32003 - 1 )
k bít đúng k nữa , thầy cko lm mà thấy nó hơi khó hỉu pn , ráng hỉu nha =))
\(S=3^0+3^2+3^4+3^6................+3^{2002}\)
\(9S=9\left(3^0+3^2+3^4+3^6+................+3^{2002}\right)\)
\(9S=3^2+3^4+3^6+3^8+.............+3^{2004}\)
\(9S-S=\left(2^2+2^4+2^6+2^8+..........+2^{2004}\right)-\left(2^0+2^2+2^4+2^6+................+2^{2002}\right)\)\(8S=2^{2004}-2^0\)
\(8S=2^{2004}-1\)
\(S=\dfrac{2^{2004}-1}{8}\)