1+1/3+1/6+11/10+.......+1/x(x+1):2=1va 1991/1993
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TN
25 tháng 11 2016
a)\(\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\)
\(\Leftrightarrow\frac{1}{3}\left(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{x\left(x+3\right)}\right)=\frac{101}{1540}\)
\(\Leftrightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1540}\)
\(\Leftrightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{303}{1540}\)\(\Leftrightarrow\frac{1}{x+3}=\frac{1}{308}\)
\(\Leftrightarrow x+3=308\Leftrightarrow x=305\)
b ko hiểu đề
NT
0
NT
0
NT
0
TM
12 tháng 4 2016
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
12 tháng 4 2016
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
12 tháng 4 2016
<=> 1/3 + 1/6 + 1/10 +...+ 1/x(x+1):2 = 1/1991/1993 - 1 = 1991/1993
<=> 1/2(2+1):2 + 1/3(3+1):2 + ...+ 1/x(x+1):2 = 1991/1993
<=> 1/2.3:2 + 1/3.4:2 +...+ 1/x(x+1):2 = 1991/1993
<=>(1/2 - 1/3):1/2 + (1/3 - 1/4 ):1/2+...+(1/x-1/x+1):1/2=1991/1993
<=>(1/2-1/3).2 + (1/3-1/4).2+...+(1/x-1/x+1).2 = 1991/1993
<=>2.(1/2-1/3+1/3-1/4+1/4-1/5+....+1/x-1/x+1)=1991/1993
<=>2.(1/2-1/x+1)=1991/1993
<=>1/2-1/x+1=1991/1993:2=1991/3986
<=> 1/x+1=1/2-1991/3986=2/3986=1/1993
=>x=1993-1=1992
12 tháng 4 2016
1+13+16+110+...+1x(x+2):2=19911993
⟹12+16+112+120+...+1x(x+2)=19911993.2
⟹11.2+12.3+13.4+14.5+...+1x.(x+2)=19911993.2
⟹1−12+12−13+14−15+...+1x−1x+2=19911993.2
⟹1−1x+2=19913986
⟹1x+2=19913986−1
⟹1x+2=−19953986
⟹x+2=−39861995
⟹x=−79761995
