Question

tính nhanh

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\)

Answer 1

Answer 2

1/6 + 1/12 + 1/20 + 1/30 + ... + 1/90

= 1/2×3 + 1/3×4 +1/4×5 + 1/5×6 + ... × 1/9×10

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/9 - 1/10

= 1/2 - 1/10

= 2/5

Answer 3

\(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{9\cdot10}\)

\(A=\frac{3-2}{2\cdot3}+\frac{4-3}{3\cdot4}+\frac{5-4}{4\cdot5}+\frac{6-5}{5\cdot6}+...+\frac{10-9}{9\cdot10}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{5-1}{10}=\frac{2}{5}.\)

Answer 4

1/6 + 1/12 + 1/20 + 1/30 + ... + 1/90

= 1/2×3 + 1/3×4 +1/4×5 + 1/5×6 + ... × 1/9×10

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/9 - 1/10

= 1/2 - 1/10

= 2/5