tính: 1/1+2+3 + 1/1+2+3+4 + 1/1+2+3+4+5 +……+ 1/1+2+3+……+2016

Giải thích các bước giải:

$\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+…..+\dfrac{1}{1+2+3+….+2016}$

$=\dfrac{1}{\dfrac{3.(3+1)}{2}}+\dfrac{1}{\dfrac{4.(4+1)}{2}}+…..+\dfrac{1}{\dfrac{2016(2016+1)}{2}}$

$=\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+…..+\dfrac{2}{2016.2017}$

$=2(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+…..+\dfrac{1}{2016.2017})$

$=2(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+……+\dfrac{1}{2016}-\dfrac{1}{2017})$

$=2(\dfrac{1}{3}-\dfrac{1}{2017})$

$=2.\dfrac{2014}{6051}$

$=\dfrac{4028}{6051}$

Chúc bạn học tốt !!!