How could we manually approximate $\sum_{i=1}^{50} i!$ to the value $ 3.1035 \times 10^{64}$?
I faced this question in my aptitude test,there were four option given,I couldn't solve it during the test,in home I used Stirling's approximation with wolfram's Mathematica to identify the correct option (if I did it right),however I am interested to know if there is any way we could do this entirely manually (probably using some tricks)?
PS:By manually I mean purely and only with pencil and paper.
ADDED: The options were:
$1)3.1035 \times 10^{65} \quad\quad 2) 3.1035 \times 10^{64} \quad\quad 3) 3.1035\times 10^{62} \quad\quad 4) 3.3339 \times 10^{62}$