Question

Tính tổng:a)  (1-1/2).(1-1/3).(1-1/4).(1-1/5)

b)(1-3/4).(1-3/7).(1-3/10).(1-3/13)...(1-3/97).(1-3/100)

2) Chứng minh)1/3+1/7+1/13+1/21+...+1/73+1/97<1

Answer 1

a)   \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}\)

\(=\frac{1}{5}\)

b)   \(\left(1-\frac{3}{4}\right).\left(1-\frac{3}{7}\right).\left(1-\frac{3}{10}\right)........\left(1-\frac{3}{97}\right).\left(1-\frac{3}{100}\right)\)

\(=\frac{1}{4}.\frac{4}{7}.\frac{7}{10}.......\frac{94}{97}.\frac{97}{100}\)

\(=\frac{1}{100}\)