Question

Cum rezolv acest exercitiu : [1/1*2+1/2*3+1/3*4 .... 1/51*52] ???

Answer 1

   
[tex]\displaystyle\\ \texttt{Folosim formula: }~~\frac{1}{n\times (n+1)}=\frac{1}{n}-\frac{1}{ (n+1)}\\\\\\ \frac{1}{1\times 2}+\frac{1}{2\times 3}+ \frac{1}{3\times 4}+\cdots + \frac{1}{50\times 51}+\frac{1}{51\times 52} =\\\\ = \frac{1}{1} - \frac{1}{2} +\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots \frac{1}{50}-\frac{1}{51}+\frac{1}{51}-\frac{1}{52} =\\\\ \texttt{Termenii se reduc cate doi in afara de primul si ultimul.}\\\\ =\frac{1}{1} -\frac{1}{52} = \boxed{\frac{51}{52} }[/tex]