a) tìm n thuộc Z để phân số sau đây là số nguyên\(\dfrac{3}{n-2}\)
b)tìm số y nguyên dương biết:\(\dfrac{3}{y}< \dfrac{y}{7}< \dfrac{4}{y}\)
c)\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+.....+\dfrac{1}{29.30}\)
d)\(\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right).\left(1-\dfrac{1}{6}\right)......\left(1-\dfrac{1}{29}\right).\left(1-\dfrac{1}{30}\right)\)
a) Để phân số \(\dfrac{3}{n-2}\) là số nguyên thì n - 2 \(⋮\) 3
\(\Rightarrow\) n - 2 \(\in\) Ư(3)
\(\Rightarrow\) n - 2 \(\in\){3; -3; 1;-1}
n \(\in\){5; -1; 3; 2}
c) \(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+......+\dfrac{1}{28.29}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+.....+\dfrac{1}{29}-\dfrac{1}{30}\)
\(=\dfrac{1}{3}-\dfrac{1}{30}\)
\(=\dfrac{10}{30}-\dfrac{1}{30}\)
\(=\dfrac{9}{30}\)
=\(\dfrac{3}{10}\)
d)\(\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right).\left(1-\dfrac{1}{6}\right).......\left(1-\dfrac{1}{29}\right).\left(1-\dfrac{1}{30}\right)\)\(=\dfrac{3}{4}.\dfrac{4}{5}.\dfrac{5}{6}....\dfrac{28}{29}\)
\(=\dfrac{3.4.5...28}{4.5.6...29}\)
\(=\dfrac{3}{29}\)
