a)A=1/20+1/30+1/42+1/56+1/72+1/90+1/110
= 1/4*5 + 1/5*6 + 1/6*7 + ... + 1/10*11
= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/10 - 1/11
= 1/4 - 1/11
= 7/44
b)B=1/2+1/4+1/6+1/8+...+1/512+1/1024
B = 1/2^1 + 1/2^2 + 1/2^3 + ... + 1/2^9 + 1/2^10
2B = 1 + 1/2 + 1/2^2 + ... + 1/2^10 + 1/2^11
2B - B = B = 1 + 1/2^11
a) Ta có: \(A=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\)
\(\Leftrightarrow A=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\)
\(\Leftrightarrow A=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(\Leftrightarrow A=\frac{1}{4}-\frac{1}{11}\)
\(\Leftrightarrow A=\frac{11-4}{44}\)
\(\Leftrightarrow A=\frac{7}{44}\)
