1/3 + 1/6 + 1/10 +............+1/x(x+1):2 =2001/2003. Tìm x
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TQ
1
7 tháng 4 2023
Ta có:
1/3 + 1/6 + 1/10 + ... + 1/x(x+1):2 = 2001/2003
=> 2/6 + 2/12 + 2/20 + ... + 2/x(x+1) = 2001/2003
=> 2 [1/6 + 1/12 + 1/20 + ... + 1/x(x+1)] = 2001/2003
=> 2 [1/2x3 + 1/3x4 + 1/4x5 + ... + 1/x+(x+1)] = 2001/2003
=> 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/x - 1/x+1= 2001/2003 : 2
=> 1/2 - 1/x+1 = 2001/4006
=> 1/x+1 = 1/2 - 2001/4006 = 1/2003
=> x+1 = 2003 = 2002 + 1
=>x = 2002
NT
0
B
2
1 tháng 4 2015
= 2/(2.3) + 2/3.4 + 2/4.5 +...+ 2/x(x+1) = 2 [1/2-1/3+1/3-1/4+...+1/x-1/(x+1)]
=2[1/2-1/(x+1)]= (x-1)/(x+1) = 2001/2003
==> x=2002
CV
0
QG
0
TT
0
16 tháng 6 2017
mik nghĩ chỗ \(\dfrac{2}{x.\left(x+1\right)}\) phải là \(\dfrac{1}{x.\left(x+1\right)}\) bạn có thể vui lòng kiểm tra lại đề không Lệ Quyên
16 tháng 6 2017
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2001}{2003}\)
\(\Leftrightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2001}{2003}\)
\(\Leftrightarrow\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2001}{2003}\)
\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2001}{4006}\)
\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{2001}{4006}\)\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{2003}\)
\(\Leftrightarrow x+1=2003\Leftrightarrow x=2002\)
NV
0
LS
2
HT
12 tháng 7 2015
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{x\left(x+1\right):2}=\frac{2001}{2003}\)
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{2001}{2003}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2001}{2003}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{2003}:2=\frac{2001}{4006}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}=\frac{1}{2003}\)
=> x+1 = 2003
=> x = 2003 - 1
=> x = 2002
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2001}{2003}\)
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2001}{2003}\)
\(2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2001}{2003}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{2003}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)
=> \(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}=\frac{1}{2003}\)
=> x + 1 = 2003
=> x = 2003 - 1
=> x = 2002
13+16+110+...+1x(x+1):2=2001200313+16+110+...+1�(�+1):2=20012003
26+212+220+...+2x(x+1)=2001200326+212+220+...+2�(�+1)=20012003
2.(12.3+13.4+14.5+...+1x(x+1))=200120032.(12.3+13.4+14.5+...+1�(�+1))=20012003
12−13+13−14+14−15+...+1x−1x+1=20012003:212−13+13−14+14−15+...+1�−1�+1=20012003:2
12−1x+1=2001400612−1�+1=20014006
=> 1x+1=12−20014006=120031�+1=12−20014006=12003
=> x + 1 = 2003
=> x = 2003 - 1
=> x = 2002