Question

Sa se arate ca: 3/2×5+3/5×8+3/8×11+...+3/2012×2015= 2013/4030

Answer 1

3/(2×5)+3/(5×8)+3/(8×11)+...+3/(2012×2015)=

=(5-2)/(2×5)+(8-5)/(5×8)+(11-8)/(8×11)+....+(2015-2012)/(2012×2015)=

=5/(2×5)-2/(2×5)+8/(5×8)-5/(5×8)+11/(8×11)-8/(8×11)+....+2015/(2012×2015)-

-2012/(2012×2015)=

=1/2-1/5+1/5-1/8+1/8-1/11+1/11+....-1/2012+1/2012-1/2015=

=1/2-1/2015=

=2015/4030-2/4030=2013/4030