Question

comparati numerele a=1 supra1x2+1supra2x3....+1supra2013x2014 si 1

Answer 1

1/k(k+1)=(k+1)-k/k(k+1)=1/k-1/k+1
a=1/1*2+1/2*3+....+1/2013*2014
a=1-1/2+1/2-1/3+1/3-1/4+.....+1/2013-1/2014
a=1-1/2014
a=2013/2014
2013/2014 <1⇒a<1
Sper ca te-am ajutat.