Đáp án:
`A=4028/2015`
Giải thích các bước giải:
`A=1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+...+2014)`
`=>`$A=1+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}$ `+ \ ...+`$\dfrac{1}{\dfrac{(2014+1).2014}{2}}$
`=>`$A=1+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}$ `+ \ ...+`$\dfrac{1}{\dfrac{2015.2014}{2}}$
`=>A/2=1/2+1/6+1/12+1/20+...+1/2014.2015`
`=>A/2=1/1.2+1/2.3+1/3.4+1/4.5+...+1/2014.2015`
`=>A/2=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2014-1/2015`
`=>A/2=1-1/2015`
`=>A/2=2014/2015`
`=>A=4028/2015`