If x = log_abc, y = log_bca, z = log_cab, then the value of $${1 \over {1 + x}} + {1 \over {1 + y}} + {1 \over {1 + z}}$$ will be

The value of $${{{{\log }_3}5 \times {{\log }_{25}}27 \times {{\log }_{49}}7} \over {{{\log }_{81}}3}}$$ is

The sum of the series $${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}} - \,\,.....\,\,\infty $$ is

If $${\log _3}x + {\log _3}y = 2 + {\log _3}2$$ and $${\log _3}(x + y) = 2$$, then