Giải thích các bước giải:
Ta có:
$A=(-\dfrac15)^0+(-\dfrac15)^1+(-\dfrac15)^2+....+(-\dfrac15)^{2015}$
$\to -\dfrac15\cdot A=(-\dfrac15)^1+(-\dfrac15)^2+(-\dfrac15)^3+....+(-\dfrac15)^{2016}$
$\to -\dfrac15A-A=(-\dfrac15)^{2016}-(-\dfrac15)^0$
$\to -\dfrac65A=(\dfrac15)^{2016}-1$
$\to \dfrac65A=1-(\dfrac15)^{2016}<1$
$\to A<\dfrac56$
$\to(-\dfrac15)^0+(-\dfrac15)^1+(-\dfrac15)^2+....+(-\dfrac15)^{2015}<\dfrac56$