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\( \Large \frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10} + \frac{1}{10 \times 13} + \frac{1}{13 \times 16} = ? \)
A) \( \Large \frac{5}{16} \)
B) \( \Large \frac{3}{16} \)
C) \( \Large \frac{7}{16} \)
D) \( \Large \frac{11}{16} \)
Correct answer:
A) \( \Large \frac{5}{16} \)
Description for Correct answer:
Given expression can be written as
\( \Large \frac{1}{3}\left[ \left(1-\frac{1}{4}\right) + \left(\frac{1}{4}-\frac{1}{7}\right) + \left(\frac{1}{7} - \frac{1}{10}\right) + \left(\frac{1}{10}-\frac{1}{13}\right) + \left(\frac{1}{13}-\frac{1}{16}\right) \right] \)
= \( \Large \frac{1}{3}\left[ 1 - \frac{1}{16} \right] = \frac{1}{3} \left(\frac{16-1}{16}\right) \)
= \( \Large \frac{1}{3} \times \frac{15}{16} = \frac{5}{16} \)
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