We see that:

\(\dfrac{1}{3.6}\)=\(\dfrac{1}{3}\). \(\dfrac{3}{3.6}\)=\(\dfrac{1}{3}\). \(\dfrac{1}{3}\)- \(\dfrac{1}{6}\)

=>A=\(\dfrac{1}{3}\). \(\dfrac{1}{3}\)- \(\dfrac{1}{6}\)+ \(\dfrac{1}{6}\)- \(\dfrac{1}{9}\)+...+\(\dfrac{1}{132}\)- \(\dfrac{1}{135}\)

       =\(\dfrac{1}{3}\). \(\dfrac{1}{3}\)- \(\dfrac{1}{135}\)

       =\(\dfrac{44}{405}\)

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A= 1/3[1/3 - 1/6 + 1/6 - 1/9 +... + 1/132 - 1/135]

= 1/3[1/3 - 1/135]

= 1/3*44/135

= 44/405