# Polynomials

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## Fractions

What is the sum of ${\frac{1}{1*4} + \frac{1}{2*5} + \frac{1}{3*6} + \frac{1}{4*7} +...}$ ?
1. ${\frac{9}{17}}$
2. ${\frac{7}{15}}$
3. ${\frac{11}{18}}$
4. ${\frac{92}{173}}$

Choice C. ${\frac{11}{18}}$

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## Detailed Solution

= ${\frac{1}{3} * [(\frac{1}{1} - \frac{1}{4}) + (\frac{1}{2} - \frac{1}{5}) + (\frac{1}{3} - \frac{1}{6}) + .. (\frac{1}{63} - \frac{1}{66}) + ..]}$
As this gives us three decreasing infinite series, we can forget about the final terms. The overall sum is = ${\frac{1}{3} * (\frac{1}{1} + \frac{1}{2} + \frac{1}{3}) = \frac{1}{3} * \frac{11}{6} = \frac{11}{18} }$

Correct Answer: ${\frac{11}{18}}$.

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