Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a= 1/1.7+4/7.13+4/13,19+4/19.25 +...+4/43.49
\(=\dfrac{1}{7}+\dfrac{4}{6}\left(\dfrac{6}{7\cdot13}+\dfrac{6}{13\cdot19}+...+\dfrac{6}{43\cdot49}\right)\)
\(=\dfrac{1}{7}+\dfrac{2}{3}\left(\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{19}+...+\dfrac{1}{43}-\dfrac{1}{49}\right)\)
\(=\dfrac{1}{7}+\dfrac{2}{3}\cdot\dfrac{6}{49}=\dfrac{1}{7}+\dfrac{4}{49}=\dfrac{11}{49}\)
\(=\dfrac{1}{7}+\dfrac{4}{6}\left(\dfrac{6}{7\cdot13}+\dfrac{6}{13\cdot19}+...+\dfrac{6}{43\cdot49}\right)\)
\(=\dfrac{1}{7}+\dfrac{2}{3}\left(\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{19}+...+\dfrac{1}{43}-\dfrac{1}{49}\right)\)
\(=\dfrac{1}{7}+\dfrac{2}{3}\cdot\dfrac{6}{49}=\dfrac{1}{7}+\dfrac{4}{49}=\dfrac{11}{49}\)