Challenge:
\((1+\frac{1}{2}) × (1+\frac{1}{3} ) × (1+ \frac{1}{4}) × (1+\frac{1}{5} ) ×\) … \(× (1+ \frac{1}{2015}) = ?\)
A- \(\frac{2015}{2014}\)
B- \(\frac{2016}{1001}\)
C- \(1008\)
D- \(2015\)
E- \(2016\)
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The correct answer is C.
Write the numbers in fraction form and simplify:
\((\frac{3}{2}) × (\frac{4}{3}) × (\frac{5}{4}) × (\frac{6}{5}) ×\) … \(× (\frac{2016}{2015}) = \frac{3×4×5×6×… ×2016}{2×3×4×5×6×… ×2015}= (\frac{2016}{2}) = 1008\)
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