Tính: 2/2+2/6+2/12+…+2/90 1/1.2+1/2.3+1/3.4+…+1/9.10

Đáp án + Giải thích các bước giải:

\(\dfrac{2}{2}\) + \(\dfrac{2}{6}\) + \(\dfrac{2}{12}\) + … + \(\dfrac{2}{90}\)

= \(\dfrac{2}{1.2}\) + \(\dfrac{2}{2.3}\) + \(\dfrac{2}{3.4}\) + … + \(\dfrac{2}{9.10}\)

= 2(\(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + … + \(\dfrac{1}{9.10}\))

= 2(1-\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) – \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) -\(\dfrac{1}{4}\) + … + \(\dfrac{1}{9}\)-\(\dfrac{1}{10}\))

= 2(1- \(\dfrac{1}{10}\))

= 2 . \(\dfrac{9}{10}\)

= $\frac{9}{5}$ 

\(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + … + \(\dfrac{1}{9.10}\)

= 1-\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) – \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) -\(\dfrac{1}{4}\) + … + \(\dfrac{1}{9}\)-\(\dfrac{1}{10}\)

= 1- \(\dfrac{1}{10}\)

= \(\dfrac{9}{10}\)