Question

e Calculați: 4/1*5 + 4/5 * 9 + 4/9*13+... +4/2013*2017 va rog frumos<3​

Answer 1

Explicație pas cu pas:

$\frac{4}{1\cdot 5} + \frac{4}{5 \cdot 9} + \frac{4}{9 \cdot 13} + ... + \frac{4}{2009 \cdot 2013} + \frac{4}{2013 \cdot 2017} =$

$= \Big(\frac{1}{1} - \frac{1}{5}\Big) + \Big(\frac{1}{5} - \frac{1}{9}\Big) + \Big(\frac{1}{9} - \frac{1}{13}\Big) + ... + \Big(\frac{1}{2009} - \frac{1}{2013}\Big) + \Big(\frac{1}{2013} - \frac{1}{2017}\Big)$

$= \frac{1}{1} - \frac{1}{5} + \frac{1}{5} - \frac{1}{9} + \frac{1}{9} - \frac{1}{13} + ... + \frac{1}{2009} - \frac{1}{2013} + \frac{1}{2013} - \frac{1}{2017}$

$= \frac{1}{1} - \frac{1}{2017} = \frac{2017 - 1}{2017} = \bf \frac{2016}{2017}$