Question

3/4.3​+3/5.4​+3/5.6​+⋯+3/90.100

Answer 1

Sửa đề: \(\dfrac{3}{4.3}+\dfrac{3}{5.4}+\dfrac{3}{5.6}+...+\dfrac{3}{99.100}\)
\(=3.\left(\dfrac{1}{4.3}+\dfrac{1}{5.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\right)\)
\(=3.\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\right)\)
\(=3.\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(=3.\left(\dfrac{1}{3}-\dfrac{1}{100}\right)\)
\(=3.\left(\dfrac{100}{300}-\dfrac{3}{300}\right)\)
\(=3.\dfrac{97}{300}\)
\(=\dfrac{97}{100}\)