Question

B=7/8+7/24+7/48+7/80+...+7/10200

Answer 1

B = \(\frac{7}{2.4}+\frac{7}{4.6}+\frac{7}{6.8}+.....+\frac{7}{100.102}\)

ta có \(\frac{7}{2.4}=\frac{1}{2}\left(\frac{7}{2}-\frac{7}{4}\right);\frac{7}{4.6}=\frac{1}{2}\left(\frac{7}{4}-\frac{7}{8}\right);......;\frac{7}{100.102}=\frac{1}{2}\left(\frac{7}{100}-\frac{7}{102}\right)\)

⇒ B = \(\frac{1}{2}\left(\frac{7}{2}-\frac{7}{4}+\frac{7}{4}-\frac{7}{8}+....+\frac{7}{100}-\frac{7}{102}\right)\)

⇔ B = \(\frac{1}{2}\left(\frac{7}{2}-\frac{7}{102}\right)\)

⇔ B = \(\frac{1}{2}.\frac{175}{51}\)

⇔ B = \(\frac{175}{102}\)