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Basic Math/Factorial and Proper fraction questions

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Rachel wrote at 2009-09-29 21:49:25
I think this problem is asking for 1/2 + 1/3 + 2/3 + 1/4 + 2/4 +3/4....99/100.



A triangular number of order n is Tn=1+2+3...+n.  Break down your sum like this:

(1/2)(1)+(1/3)(1+2)+(1/4)(1+2+3)...



Now you can see you have the sum of (1/(n+1))(Tn) from n=1 to 100.  Luckily, a triangular number Tn=n(n+1)/2.  Substituting this in we have

(1/(n+1))(n(n+1)/2)



The n+1's cancel and you're left with the sum n/2 from n=1 to 100.  we have 1/2 + 2/2 + 3/2... so we can combine with the common denominator and say that (1+2+3...100)/2.



Recall that (1+2+3...100) is a Triangular number of order 100, and is equal to [(100)(101)]/2.  This yields 5,050 as your numerator, divide by two again for the proper answer 2,525.



It's so hard to type it!  Wish we were in a classroom with a chalkboard!!  Hope this helps a little.



Best Regards,

Rachel


calc guy wrote at 2013-09-04 00:14:14
This is a retarded answer, because 1005! is divisible by more than 1000..... it's a factorial. You have to count the number of 5's in 1005! because 5x2 is 10 and there are less 5's than 2's in 1005!. "Expert" my @ss


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