Question

Efectuati 1/1x2 +1/2x3+...+1/49x50 Ajutor

Answer 1

 

$\displaystyle\\\\\text{Folosim formula: }~~~\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}\\\\\text{Rezolvare:}\\\\\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{48\times49}+\frac{1}{49\times50}=\\\\=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{48}-\frac{1}{49}+\frac{1}{49}-\frac{1}{50}=\\\\\text{Se reduc termenii asemenea.}\\\\=\frac{1}{1}-\frac{1}{50}=\boxed{\bf\frac{49}{50}}$