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- \(\dfrac{1}{10}\)
= \(\dfrac{9}{10}\)
