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Find the value of \(\frac{1}{4} + \frac{1}{{28}} + \frac{1}{{70}} + \frac{1}{{130}} + \frac{1}{{208}}\)
- A\(\frac{3}{{16}}\)
- B\(\frac{7}{{16}}\)
- C\(\frac{5}{{16}}\)
- D\(\frac{1}{{210}}\)
Answer not set
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CCommunity
$(\frac{1}{4} + \frac{1}{{28}} + \frac{1}{{70}} + \frac{1}{{130}} + \frac{1}{{208}})$
$( \Rightarrow {\rm{\;}}\frac{1}{{1{\rm{\;}} \times {\rm{\;}}4}} + \frac{1}{{4\; \times 7}} + \frac{1}{{7\; \times 10}} + \frac{1}{{10\; \times 13}} + \frac{1}{{13\; \times 16}})$
$( \Rightarrow {\rm{\;}}\frac{1}{3}(\frac{3}{{1{\rm{\;}} \times {\rm{\;}}4}} + \frac{3}{{4\; \times 7}} + \frac{3}{{7\; \times 10}} + \frac{3}{{10\; \times 13}} + \frac{3}{{13\; \times 16}}))$
$( \Rightarrow {\rm{\;}}\frac{1}{3}\;\left( {\;1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{10}} + \frac{1}{{10}} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{16}}} \right))$
$( \Rightarrow {\rm{\;}}\frac{1}{3}\; \times \frac{{15}}{{16}})$
$( \Rightarrow {\rm{\;}}\frac{5}{{16}})$
$( \Rightarrow {\rm{\;}}\frac{1}{{1{\rm{\;}} \times {\rm{\;}}4}} + \frac{1}{{4\; \times 7}} + \frac{1}{{7\; \times 10}} + \frac{1}{{10\; \times 13}} + \frac{1}{{13\; \times 16}})$
$( \Rightarrow {\rm{\;}}\frac{1}{3}(\frac{3}{{1{\rm{\;}} \times {\rm{\;}}4}} + \frac{3}{{4\; \times 7}} + \frac{3}{{7\; \times 10}} + \frac{3}{{10\; \times 13}} + \frac{3}{{13\; \times 16}}))$
$( \Rightarrow {\rm{\;}}\frac{1}{3}\;\left( {\;1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{10}} + \frac{1}{{10}} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{16}}} \right))$
$( \Rightarrow {\rm{\;}}\frac{1}{3}\; \times \frac{{15}}{{16}})$
$( \Rightarrow {\rm{\;}}\frac{5}{{16}})$