Question

tính tổng A=1/30+1/42+1/56+1/72+...+1/380

Answer 1

\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{380}=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{19.20}\)

=> \(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{5}-\frac{1}{20}\)

=> \(A=\frac{3}{20}\)

Answer 2

A = 1/30 + 1/42 + 1/56 + 1/72 +....+ 1/380

A = 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 +.....+1/19x20

A = 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 +......+ 1/19 - 1/20

A = 1/5 - 1/20 = 3/20