Question

Simplify (1+3+5+...+199)/(2+4+6+...+200). Thanks!

Answer 1

notice anything special about the numerator and the denominator?

Answer 2

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

Answer 3

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

Answer 4

yes, how does that help though?

Answer 5

oh, is the answer 2 then?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

thanks