SOLUTION: I need help with writing a sigma notation of 1/2 + 3/4 + 5/6 + ... 99/100, but I keep on getting lost and going in circles.

The denominators are the even natural numbers 2,4,6,8, and the pattern is 2n for n = 1,...,50

The numerators are 1 less than the denominators, 1,3,5,7, so we subtract 1
from that pattern 2n-1,

So the nth term is , where n goes from 1 to 50, so we can write that as
 


We can simplify, if desired:

 =  = 1 - , so we write the summation as



and if we like we can distribute the summation as

 

Then the first summation is just the sum of 50 ones, which is just 50.
So we can simplify it to



Edwin