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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

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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