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Ta có: 1/1.2 = 1/1 - 1/2 ; 1/2.3 = 1/2 - 1/3 ; 1/3.4 = 1/3 - 1/4 ; ...;1/99.100 = 1/99 - 1/100
Như vậy thì bài toán trên = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/99 - 1/100
Vậy tổng trên là:
1 - 1/100
= 99/100
tk nha
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}+1\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}+1\)
\(=1-\frac{1}{1000}+1\)
\(=\frac{1000}{1000}-\frac{1}{1000}+\frac{1000}{1000}\)
\(=\frac{1999}{1000}\)
Tham khảo nhé~
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{149.150}\)
\(A=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{149}-\dfrac{1}{150}\)
\(A=\dfrac{1}{1}-\dfrac{1}{150}\)
\(A=\dfrac{150}{150}-\dfrac{1}{150}\)
\(A=\dfrac{149}{150}\)
A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}\)
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}\)
A=\(1-\frac{1}{4}\)
A=\(\frac{3}{4}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}=\frac{6}{12}+\frac{2}{12}+\frac{1}{12}=\frac{9}{12}=\frac{3}{4}\)
1/1.2+1/2.3+1/3.4+...+1/2005.2006=(1-1/2)+(1/2-1/3)+...+(1/2005-1/2006)=1-1/2+1/2-1/3+...+1/2005-1/2006
=1-(1/2-1/2)+...-1/(1/2005-1/2005)-1/2006=1-1/2006=2005/2006
k mình nha
A= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2018.2019}\)
A= 1 - \(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{2018}-\frac{1}{2019}\)
A= 1 - \(\frac{1}{2019}\)
A= \(\frac{2018}{2019}\)
3A=1.2.3+2.3.3+...+n(n+1).3
3A=1.2(3-0)+2.3(4-1)+...+n(n+1)[(n+2)-(n-1)]
3A=(1.2.3-0.1.2)+(2.3.4-1.2.3)+...+[n(n+1)(n+2)-(n-1)n(n+1)]
3A=n(n+1)(n+2)
A=\(\frac{n\left(n+1\right)\left(n+2\right)}{3}\)
Ta có:A: 1/1.2 +1/2.3 +1/3.4+...+1/18.19+1/19.20
=> A= 1-1/2 +1/2-1/3+1/3-1/4+...+1/18-1/19+1/19-1/20
=>A= 1-1/20=19/20
\(\frac{1313}{1212}:x=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\)\(\frac{1}{5.6}\)
\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Leftrightarrow\frac{13}{12}:x=1-\frac{1}{6}\)
\(\Leftrightarrow\frac{13}{12}:x=\frac{5}{6}\)
\(\Leftrightarrow x=\frac{13}{12}:\frac{5}{6}\)
\(\Leftrightarrow x=\frac{13}{10}\)
Vậy \(x=\frac{13}{10}\)
~~~~~Hok tốt ~~~~~
a,\(\frac{1313}{1212}\div x=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(\frac{13}{12}\div x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\frac{13}{12}\div x=1-\frac{1}{6}\)
\(\frac{13}{12}\div x=\frac{5}{6}\)
\(x=\frac{13}{12}\div\frac{5}{6}\)
\(x=\frac{13}{12}\times\frac{6}{5}\)
\(x=\frac{13}{10}\)
Chúc bạn hok tốt !
A=1/1.2+1/2.3+1/3.4+..+1/99.100
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100
\(\frac{99}{100}\)