[1-1/2]*[1-1/3]*[1-1/4]*.........*[1-1/1996]*[1-1/1997]
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câu 1:
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
\(\hept{\begin{cases}15=3\cdot5\\35=5\cdot7\end{cases}}\\ \hept{\begin{cases}3=3\\63=3^2\cdot7\\99=3^2\cdot11\end{cases}}\)
=>\(\frac{2310}{3465}+\frac{462}{3465}+\frac{198}{3465}+\frac{110}{3465}+\frac{70}{3465}\)
=>\(\frac{2310+462+198+110+70}{3465}\)
=>\(\frac{3150}{3465}\)=\(\frac{10}{11}\)
( 1 - 1/2 ) x ( 1 - 1/3 ) x ( 1 - 1/4 ) x .... x ( 1 - 1/1996 ) x ( 1 - 1/1997 )
= 1/2 x 2/3 x 3/4 x .... x 1995/1996 x 1996/1997
= 1 x 2 x 3 x 4 x .... x 1995 x 1996 / 2 x 3 x 4 x .... x 1996 x 1997
= 1/1997
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(1-1/2)x(1-1/3)x(1-1/4)x....x(1-1/1996)x(1-1/997)
=1/2x2/3x3/4x....x1995/1996x1996/1997
=1x2x3x...x1995x1996/2x3x4x...x1996x1997
=1/1997
\(\Rightarrow\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{1996}{1997}\)
\(\Leftrightarrow1x\frac{1}{1997}\)\(=\frac{1}{1997}\)
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
Tính kết quả từng ngoặc rồi loại nhx số giống nhau trên tử và dưới mẫu là xong thôi mà bạn ._.
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{1997}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{1996}{1997}\)
\(=\frac{1}{1997}\)