1*2*3*4*5.......1996*1997.Bằng bao nhiêu?
1,Tính nhanh a,16×23+35×34+4×108+7×30 b,198×1996+1997×11+1985 ———————————— 1997 × 1996 - 1995 × 1996 c,1/2+2/8+3/28+4/77+5/176
a) A=1-2-3+4+5-6-7+.....+1996+1997-1998-1999+2000
b) B=1-3+5-7+....+2001-2003+2005
c) C=1-2-3+4+5-6-7+8+.....+1993-1994-1995+1996+1997
d) D=1000+998+996+......+10-999-997-995-...-11
a) A=1-2-3+4+5-6-7+.....+1996+1997-1998-1999+2000
=(1-2-3+4)+(5-6-7+8)+...+(1997-1998-1999+2000)
=0
b) B=1-3+5-7+....+2001-2003+2005
=(1-3)+(5-7)+...+(2001-2003)+2005
=-2.501+2005
=-1002+2005
=1003
c) C=1-2-3+4+5-6-7+8+.....+1993-1994-1995+1996+1997
=(1-2-3+4)+(5-6-7+8)+...+(1993-1994-1995+1996)+1997
=1997
d) D=1000+998+996+......+10-999-997-995-...-11
=(1000-999)+(998-997)+(996-995)+....+(12-11)+10
=1.495+10
=595
M= 1-2-3+4+5-6-7+8+...........+1993-1994-1995+1996+1997.
tìm x sao cho : (x+5)/1995+ (x+4)/1996+ (x+3)/1997 = (x+1995)/5 + (x+1996)/4 + (x+1997)/3
giúp mik với, đúng mik tick cho nha
cộng 1 vào mỗi tỉ số,ta đc:
(x+5)/1995+1+(x+4)/1996+1+(x+3)/1997+1=(x+1995)/5+1+(x+1996)/4+1+(x+1997|/3+1
=>\(\frac{x+5+1995}{1995}+\frac{x+4+1996}{1996}+\frac{x+3+1997}{1997}=\frac{x+1995+5}{5}+\frac{x+1996+4}{4}+\frac{x+1997+3}{3}\)
\(\Rightarrow\frac{x+2000}{1995}+\frac{x+2000}{1996}+\frac{x+2000}{1997}-\frac{x+2000}{5}-\frac{x+2000}{4}-\frac{x-2000}{3}=0\)
\(\Rightarrow\left(x+2000\right)\left(\frac{1}{1995}+\frac{1}{1996}+\frac{1}{1997}-\frac{1}{5}-\frac{1}{4}-\frac{1}{3}\right)=0\)
mà bt trong ngoặc thứ 2 khác 0
=>x+2000=0
=>x=-2000
1-2-3+4+5-6-7+...+1996+1997-1998-1999+2000+2001
[1-2-3+4]+........+[1997-1998-1999+2000]+2001
=0+0+....+0+2001
=2001
[1-2-3+4]+........+[1997-1998-1999+2000]+2001
=0+0+....+0+2001
=2001
Tinh nhanh: M=1-2-3+4+5-6-7+8+...+1993-1994-1995+1996+1997
Tính nhanh: M=1-2-3+4+5-6-7+8+...+1993-1994-1995+1996+1997
(1-2-3+4)+(5-6-7+8)+.....+(1993-1994-1995+1996)+1997
=0+0+....+0+1997
=1997
Tính nhanh:
M=1-2-3+4+5-6-7+8+...+1993-1994-1995+1996+1997
Tìm x, biết
\(\frac{x+5}{1995}+\frac{x+4}{1996}+\frac{x+3}{1997}=\frac{x+1995}{5}+\frac{x+1996}{4}+\frac{x+1997}{3}\)
ta có \(1+\frac{x+5}{1995}+1+\frac{x+4}{1996}+1+\frac{x+3}{1997}=1+\frac{x+1995}{5}+1+\frac{x+1996}{4}+1+\frac{x+1997}{3}\)
\(=\frac{x+2000}{1995}+\frac{x+2000}{1996}+\frac{x+2000}{1997}=\frac{x+2000}{5}+\frac{x+2000}{4}+\frac{x+2000}{3}\)
\(=\left(x+2000\right)\left(\frac{1}{1995}+\frac{1}{1996}+\frac{1}{1997}\right)=\left(x+2000\right)\left(\frac{1}{5}+\frac{1}{4}+\frac{1}{3}\right)\) (1)
Xét \(\frac{1}{1995}+\frac{1}{1996}+\frac{1}{1997}\ne\frac{1}{5}+\frac{1}{4}+\frac{1}{3}vàx+2000=x+2000\) (2)
từ \(\left(1\right)\Leftrightarrow x+2000=0\) ( để (1) là đúng )
\(\Rightarrow x=2000\)