Đáp án+Giải thích các bước giải:
$\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+....+\dfrac{1}{98.99.100}\\=\dfrac{1}{2}.\left(\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+....+\dfrac{2}{98.99.100}\right)\\=\dfrac{1}{2}.\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac1{3.4}+....+\dfrac{1}{98.99}-\dfrac1{99.100}\right)\\=\dfrac{1}{2}.\left(\dfrac12-\dfrac1{9900}\right)\\=\dfrac12.\dfrac{4949}{9900}\\=\dfrac{4949}{19800}$
