Question

Va rog sa ma ajutati! simplificati fractia din imagine

Answer 1

$\frac{1+2+3+...+2015}{1+2+3+...+2014}=\frac{1+2+3+...+2014}{1+2+3+...+2014}+\frac{2015}{1+2+3+...+2014}=Prima~fractie~este~1=1+\frac{2015}{\frac{2014*2015}{2}} =1+2015*\frac{2}{2014*2015} = Se~simplifica~2015~cu~2015=1+\frac{2}{2014}=1+\frac{1}{1007}=\frac{1007+1}{1007}=\frac{1008}{1007}$

Answer 2

$\it 1+2+3+ ... +2015=\dfrac{2015\cdot2016}{2} = 2015\cdot1008 \\ \\ \\ 1+2+3+ ... +2014=\dfrac{2014\cdot2015}{2} = 2015\cdot1007 \\ \\ \\ F = \dfrac{2015\cdot1008}{2015\cdot1007} =\dfrac{1008}{1007}$