Tinh nhanh
2002 × 2002 +1
2003 × 2002 - 2002
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Vì 2002 = 2002
Mà 2002 < 2004
=> 2002.2002 < 2002.2004
Tinh nhanh
2003×14+1998+2001×2002 / 2002+2002×503+504×2003
Viet ro loi giai nhe! Ai nhanh mk tk cho!
2003x14+1998+2001x2002/2002+2002x503+504x2003 =2003x14+1998+2001x1+2002x503+504x2003 =2003x14+1998+2001+2002x503+504x2003 =28042+1998+2001+1007006+1009512 =(28042+1009512+1007006)+1998+2001 =2044560+1998+2001=2048559 TK MIk nha bn! mk tra loi dau tien ma ! Giu loi hua nhe!
2003 x 14 + 1988 + 2001 x 2002
=28042 + 1988 + 4006002
=4036032
2002 + 2002 x 503 +504 x 2002
=2002 x 1 + 2002 x 503 + 504 x 2002
=2002 x (1 + 503 + 504)
=2002 x 908
=1817816
(72003 + 72002) : 72002
= (72003 + 72002) . 1/72002
\(=\frac{7^{2003}}{7^{2002}}+\frac{7^{2002}}{7^{2002}}=7+1=8\)
A=2002.2002
A=(2000+2).2002
A=2000.2002+2002.2
B=2000.2004
B=2000.(2002+2)
B=2000.2002+2000.2
Vì 2000.2002=2000.2004; 2002.2>2000.2
=>2000.2002+2002.2> 2000.2004+2000.2
hay A>B
Vậy A>B
\(A=\left(\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{4!}+...+\frac{2002-1}{2002!}\right)+\frac{1}{2002!}\)
\(A=\left(\frac{2}{2!}-\frac{1}{2!}+\frac{3}{3!}-\frac{1}{3!}+\frac{4}{4!}-\frac{1}{4!}+...+\frac{2002}{2002!}-\frac{1}{2002!}\right)+\frac{1}{2002!}\)
\(A=\left(\frac{1}{1!}-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}-\frac{1}{4!}+...+\frac{1}{2001!}-\frac{1}{2002!}\right)+\frac{1}{2002!}\)
\(A=\frac{1}{1!}-\frac{1}{2002!}+\frac{1}{2002!}=1\)
a = 2002 . 2002
a = (2000 + 2) . 2002
a = 2000.2002 + 2.2002
b = 2000 . 2004
b = 2000 . (2002 + 2)
b = 2000.2002 + 2.2000
Vì 2002 > 2000
=> 2.2002 > 2.2000
=> 2000.2002 + 2.2002 > 2000.2002 + 2.2000
=> a > b
\(=\frac{2002x2002+1}{2002\left(2003-1\right)}=\frac{2002x2002+1}{2002x2002}=1+\frac{1}{2002x2002}\)