Tính nhanh 1998^2-1997(1998+1)
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\(=\left(1999\times1998+1998\times1997\right)\times\left(1+\dfrac{1}{2}:1\dfrac{1}{2}-1\dfrac{1}{3}\right)\)
\(=\left(1999\times1998+1998\times1997\right)\times\left(1+\dfrac{1}{2}:\dfrac{3}{2}-\dfrac{4}{3}\right)\)
\(=\left(1999\times1998+1998\times1997\right)\times\left(1+\dfrac{1}{3}-\dfrac{4}{3}\right)\)
\(=\left(1999\times1998+1998\times1997\right)\times\left(\dfrac{4}{3}-\dfrac{4}{3}\right)\)
\(=\left(1999\times1998+1998\times1997\right)\times0\)
\(=0\)
1996 x 1997 + 1998 x 3 + 1994 / 1997 x 1999 - 1997 x 1997
= 1996 x 1997 + ( 1997 + 1 x 3 ) + 1994 / 1997 x 1999 - 1997 x 1997
= 1996 x 1998 + 1 x 3 + 1994 / 1997 x 1999 - 1997 x 1997
= 3988008 + 3 + 1994 / 1997 x 1999 - 1997 x 1997
= 3990005 / 1997 x 1999 - 1997 x 1997
= 3990005 / ( 1999 - 1997 ) x 1997
= 3990005 / 3994
Ta có: 1-2-3+4+5-6-7+...+1997-1998-1999+2000+2001
=(1-2-3)+[4+(5-6-7)]+[8+(9-10-11)]+...+[1996+(1997-1998-1999)]+(2000+2001)
Từ 4 đến 1999 có số số hạng là: (1999-4):1+1=1996(số hạng)
= -4 + [4+(-8)] + [8+(-12)] + [12+(-16)] + ... + [1996+(-2000] + 4001
= -4 + (-4) + (-4) + (-4) + ... + (-4) + 4001
= -4 + (-4).(1996:4) + 4001
= -4 + (-4).499 + 4001
= -4.500 + 4001
= -2000 + 4001
= 2001
Nhớ k
B = (1999x1998 + 1998x1997)x(1+1/2: 1 1/2 - 11/3)
B = (1999x1998 + 1998x1997)x(1+1/2:3/2-4/3)
B = (1999x1998 +1998 x1997) x (1+1/2x2/3 - 4/3)
B = (1999 x 1998 + 1998 x 1997) x(1+1/3 - 4/3)
B = (1999 x 1998 + 1998 x 1997) x (4/3 - 4/3)
B = (1999 x 1998 + 1998 x 1997) x 0
B = 0
B = (1999x1998 + 1998x1997)x(1+1/2: 1 1/2 - 11/3)
B = (1999x1998 + 1998x1997)x(1+1/2:3/2-4/3)
B = (1999x1998 +1998 x1997) x (1+1/2x2/3 - 4/3)
B = (1999 x 1998 + 1998 x 1997) x(1+1/3 - 4/3)
B = (1999 x 1998 + 1998 x 1997) x (4/3 - 4/3)
B = (1999 x 1998 + 1998 x 1997) x 0
B = 0
\(\dfrac{1996\cdot1997+\left(1997+1\right)\cdot3+1994}{1997\cdot\left(1999-1997\right)}\) = \(\dfrac{1996\cdot1997+3\cdot1997+1997}{1997\cdot2}\)
\(\dfrac{1997\cdot\left(1996+3+1\right)}{1997\cdot2}\) = \(\dfrac{2000}{2}\)= \(1000\)
1998^2-1997(1998+1)
=1998^2-(1998-1)(1998+1)
=1998^2-(1998^2-1)
=1998^2-1998^2+1
=1