A = 1/2 + 1/6 + 1/12 + ... + 1/6480
A = 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/80.81
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/80 - 1/81
A = 1 - 1/81
A = 80/81
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{6480}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{80.81}\)
\(=1.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+...+\frac{1}{80}.\frac{1}{81}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+...+\frac{1}{80}-\frac{1}{81}\)
\(=1-\frac{1}{81}\)
\(\Rightarrow A=\frac{80}{81}\)
A=1/2 + 1/6 + 1/12 +...+ 1/6480
A = 1/2.1 + 1/2.3 + 1/3.4 + ... + 1/80.81
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/80 - 1/81
A = 1 - 1/81
A = 80/81
Vậy A = 80/81
A = \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{6320}+\frac{1}{6480}=\)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{79.80}+\frac{1}{80.81}\)
= \(\frac{2}{1.2}-\frac{1}{1.2}+\frac{3}{2.3}-\frac{2}{2.3}+\frac{4}{3.4}-\frac{3}{3.4}+...+\frac{80}{79.80}-\frac{79}{79.80}+\frac{81}{80.81}\)\(-\frac{80}{80.81}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{79}-\frac{1}{80}+\frac{1}{80}-\frac{1}{81}\)= \(1-\frac{1}{81}=\frac{80}{81}\)
A = 1/2+ 1/6 + 1/12 + ... + 1/6480
A = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/80x81
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 + 1/4 + ... + 1/80 - 1/81
A = 1 - 1/81
A = 80/81
A = 1/2 + 1/6 + 1/12 + ... + 1/6480
A = 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/80.81
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/80 - 1/81
A = 1 - 1/81
A = 81/81 - 1/81
A = 80/81
