Question

Tính nhanh :\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{1225}\)\

Giúp mình với....chiều phải nộp bài r

Answer 1

Đặt : \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{1225}\)

\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{2450}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{49.50}\)

\(A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{49}-\frac{1}{50}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{50}\right)\)

\(A=2.\frac{12}{25}\)

\(A=\frac{24}{25}\)