Giải:
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2009.2011}.\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\right).\)
\(=\dfrac{1}{2}\left[\left(\dfrac{1}{3}-\dfrac{1}{3}\right)+\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+...+\left(\dfrac{1}{2009}-\dfrac{1}{2009}\right)+\left(1-\dfrac{1}{2011}\right)\right].\)
\(=\dfrac{1}{2}\left[0+0+0+...+\left(1-\dfrac{1}{2011}\right)\right].\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{2011}\right).\)
\(=\dfrac{1}{2}.\dfrac{2010}{2011}=\dfrac{2010}{4022}=\dfrac{1005}{2011}.\)
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Bài mik đúng thì nhớ tick mik nha!!!
1\1-1\3+1\3-1\5+1\5-1\7+...+ 1\2009- 1\2011
=1- 1\2011
=2010\2011
dấu \ là 1 trên 
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{2009.2011}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\)
\(=1-\dfrac{1}{2011}\)
\(=\dfrac{2010}{2011}\)
\(\dfrac{1}{1.3}\) + \(\dfrac{1}{3.5}\)+ ...+ \(\dfrac{1}{2009.2011}\) = 1-\(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + ... + \(\dfrac{1}{2009}\) - \(\dfrac{1}{2011}\) = 1- \(\dfrac{1}{2011}\) den day ban tu tinh nha
Tom lai la ai dung vay ban Tran Thi My Tam ?
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2009.2011}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{2009.2011}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2009}-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{2011}\right)\)
\(=\dfrac{1}{2}.\dfrac{2010}{2011}\)
\(=\dfrac{1005}{2011}\)
Nói chung là tôi cho mỗi người 1 like.
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