1.

1). \(\frac{{3}}{4}\)2). \(\frac{5}{8}\)3). \(\frac{3}{16}\)4). \(\frac{3}{8}\)

Answer»

$(\begin{array}{l} \Rightarrow \FRAC{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}}\\ \Rightarrow \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + \frac{1}{{5 \times 6}} + \frac{1}{{6 \times 7}} + \frac{1}{{7 \times 8}}\\ \Rightarrow \LEFT( {\frac{1}{2}-\frac{1}{3}} \RIGHT) + \left( {\frac{1}{3}-\frac{1}{4}} \right) + \left( {\frac{1}{4}-\frac{1}{5}} \right) + \left( {\frac{1}{5}-\frac{1}{6}} \right) + \left( {\frac{1}{6}-\frac{1}{7}} \right) + \left( {\frac{1}{7}-\frac{1}{8}} \right)\\ \Rightarrow \frac{1}{2}-\frac{1}{3} + \frac{1}{3}-\frac{1}{4} + \frac{1}{4}-\frac{1}{5} + \frac{1}{5}-\frac{1}{6} + \frac{1}{6}-\frac{1}{7} + \frac{1}{7}-\frac{1}{8}\\ \Rightarrow \frac{1}{2}-\frac{1}{8}\\ \Rightarrow \frac{{4-1}}{8}\\\therefore \frac{3}{8}\end{array})$



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