Aren't they the same?

Algebra Level pending

\[ \begin{eqnarray} \displaystyle A &=& \frac1{2\times32} + \frac1{3\times33} + \ldots + \frac1{n\times(n+30)} + \frac1{1979\times2009} \\ \displaystyle B &=& \frac1{2\times1980} + \frac1{3\times1981} + \ldots + \frac1{n\times(n+1978)} + \frac1{1979\times2009} \\ \end{eqnarray} \]

What is the value of \( \frac B A\)?

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