What is the number of trailing zeros in (10^10)!!. Note that "!!" is the double factorial function. Please just give me a hint and I will do the homework! Ridiculous question by our teacher. I thank you for any help.
That is a very big number!! But, there is a method to your teacher's madness!! Since you are willing to do the homework, I will give you a hint and you finish the job!.
Take 10^10 and divide it by the powers of 5 as follows:
(10^10) / 5 + (10^10) / 5^2 + (10^10) / 5^3 + ............+ (10^10) / 5^14.
Note: It is very important that you divide them one at a time and take the INTEGER PART ONLY. Disregard the fractional part. Once you calculate them all, then add them up and DIVIDE THE TOTAL BY 2. Again, if there is a fraction, disregard it and keep the integer part only. That should give you a lot of zeros!!. Good Luck.
