Many calculators or computers cannot directly calculate 70 ! or higher. When $ \mathrm{n} $ is large, $ \mathrm{n} $ ! can be approximated by $ \mathrm{n} !=10^{\mathrm{K}} $, where $ \mathrm{K}=(\mathrm{n}+0.5) \log n+0.39908993-0.43429448 \mathrm{n} $. Evaluate 79 ! using the approximation given above.
A) $ 8.937 \times 10^{116} $
B) $ 1.005 \times 10^{116} $
C) $ 2.890 \times 10^{313} $
D) $ 1.170 \times 10^{2} $

Question

Quizplus · Accepted Answer

Using the given formula $ \mathrm{K}=(\mathrm{n}+0.5) \log n+0.39908993-0.43429448 \mathrm{n} $ for $ n = 79 $, we calculate $ K $ and then use $ 10^K $ to approximate $ 79! $. The calculation aligns closest with option A, $ 8.937 \times 10^{116} $, when following the approximation method provided.

Many Calculators or Computers Cannot Directly Calculate 70 ! or Higher