Question

Tính tổng 

A = 1/3 +1/15+1/35+1/63+......+1/143

Answer 1

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{11.13}\)

\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)

\(A=1-\frac{1}{13}\)

\(A=\frac{12}{13}\)

Answer 2

A = 1/3 + 1/15 + 1/35 + 1/63 +.....+ 1/143

   = 1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 +.....+1/11.13

   = 1/2 . (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 +...+ 1/11 - 1/13)

   = 1/2 . (1 - 1/13)

   = 1/2 . 12/13

   = 6/13