## zmudz one year ago Simplify (1+3+5+...+199)/(2+4+6+...+200). Thanks!

1. Vocaloid

notice anything special about the numerator and the denominator?

2. zmudz

it is all odd numbers to 199 and all even numbers to 200

3. Vocaloid

yes, but more specifically, every number in the denominator is just + 1 greater than every number in the numerator, correct?

4. zmudz

yes, how does that help though?

5. zmudz

oh, is the answer 2 then?

6. zmudz

whoops, that was stupid, i think I know the answer now. thank you!

7. anonymous

you could simplify it by using sum formula for arithmetic series $S = \frac{n (a_1 + a_n)}{2}$

8. Vocaloid

this probably won't be read by anyone, but eh... we have 100 terms in the numerator and 100 terms in the denominator we can calculate the sum 1 + 3 + ... 199 using the formula above, and represent this sum as S if we let the numerator equal S, then the denominator is S + 100, since there are 100 terms in the denominator and each term is 1 greater than its corresponding term in the numerator so our answer is something along the lines of S/(S+100) which allows use to use the sum formula once instead of twice

9. Vocaloid

^meant to post that earlier, got sidetracked by another question

10. zmudz

thanks