a: A=1/2+1/4+...+1/1024
=>2A=1+1/2+...+1/512
=>2A-A=1-1/1024=1023/1024
=>A=1023/1024
b: \(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
=1-1/100=99/100
c: \(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}\)
=1/2-1/11
=9/22