Summer Clouds moderators
25/08/2017 at 15:49-
Help you solve math 25/08/2017 at 15:56\(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\)
=\(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\)
=\(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) -\(\dfrac{1}{5}\) +\(\dfrac{1}{5}\) - \(\dfrac{1}{6}\)
=\(\dfrac{1}{1}\) - \(\dfrac{1}{6}\)
=\(\dfrac{5}{6}\)
Selected by MathYouLike -
= \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{5.6}\)
= \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{5}-\dfrac{1}{6}\)
= \(\dfrac{1}{1}-\dfrac{1}{6}=\dfrac{5}{6}\)
-
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\dfrac{1}{1}-\dfrac{1}{6}=\dfrac{5}{6}\)