1/1+2 + 1/+1+2+3 + ... + 1/1+2+3+...+2014
= 1/(1+2).2:2 + 1/(1+3).3:2 + ... + 1/(1 + 2014).2014:2
= 2/2.3 + 2/3.4 + ... + 2/2014.2015
= 2.(1/2.3 + 1/3.4 + ... + 1/2014.2015)
= 2.(1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2014 - 1/2015)
= 2.(1/2 - 1/2015)
= 2.1/2 - 2.1/2015
= 1 - 2/2015
= 2013/2015
1/1+2 + 1/+1+2+3 + ... + 1/1+2+3+...+2014
= 1/(1+2).2:2 + 1/(1+3).3:2 + ... + 1/(1 + 2014).2014:2
= 2/2.3 + 2/3.4 + ... + 2/2014.2015
= 2.(1/2.3 + 1/3.4 + ... + 1/2014.2015)
= 2.(1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2014 - 1/2015)
= 2.(1/2 - 1/2015)
= 2.1/2 - 2.1/2015
= 1 - 2/2015
= 2013/2015