Question

Sa se determine x € Z astfel incat :
S= x/1+2 + ×/1+2+3 +......+ x/1+2+3+.....+2015

Answer 1

[tex]S=\frac{x}{1+2}+\frac{x}{1+2+3}+...+\frac{x}{1+2+3+...+2015}\\ S=x(\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+...+\frac{2}{2015\cdot 2016})\\ S=2x(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2015}-\frac{1}{2016})\\ S=2x(\frac{1}{2}-\frac{1}{2016})\\ S=2x\cdot \frac{1007}{2016}\\ S=\frac{1007x}{1008}\\ Acesta\ este\ raspunsul\ final.[/tex]