Evaluate: $$\frac{1}{{15}} + \frac{1}{{35}} + \frac{1}{{63}} + \frac{1}{{99}} + \frac{1}{{143}}$$
A. $$\frac{4}{{39}}$$
B. $$\frac{5}{{39}}$$
C. $$\frac{{10}}{{39}}$$
D. $$\frac{7}{{39}}$$
Answer: Option B
Solution (By Examveda Team)
$$\eqalign{ & \frac{1}{{15}} + \frac{1}{{35}} + \frac{1}{{63}} + \frac{1}{{99}} + \frac{1}{{143}} \cr & = \frac{1}{2}\left[ {\frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7}\,.\,.\,.\,.\,.\,\frac{1}{{11}} - \frac{1}{{13}}} \right] \cr & = \frac{1}{2}\left[ {\frac{1}{3} - \frac{1}{{13}}} \right] \cr & = \frac{1}{2} \times \frac{{10}}{{39}} \cr & = \frac{5}{{39}} \cr} $$This Question Belongs to Arithmetic Ability >> Simplification
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