Calculati partea intreaga a nr a=1/(1*2)+1/(2*3)+.....+1/(9*10)
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[tex]\text{Forma generala:}\boxed{\dfrac{1}{n(n+1)}=\dfrac{1}{n}-\dfrac{1}{n+1}}\\
a=\dfrac{1}{1\cdot 2}+\dfrac{1}{2\cdot 3}+_{\dots}\dfrac{1}{9\cdot 10}\\
a=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+_{\dots}+\dfrac{1}{9}-\dfrac{1}{10}\\
a=1-\dfrac{1}{10}\\
a=\dfrac{9}{10}\\
0\ \textless \ \dfrac{9}{10}\ \textless \ 1\Rightarrow [a]=0[/tex]
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