zmudz
  • zmudz
Simplify (1+3+5+...+199)/(2+4+6+...+200). Thanks!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Vocaloid
  • Vocaloid
notice anything special about the numerator and the denominator?
zmudz
  • zmudz
it is all odd numbers to 199 and all even numbers to 200
Vocaloid
  • Vocaloid
yes, but more specifically, every number in the denominator is just + 1 greater than every number in the numerator, correct?

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zmudz
  • zmudz
yes, how does that help though?
zmudz
  • zmudz
oh, is the answer 2 then?
zmudz
  • zmudz
whoops, that was stupid, i think I know the answer now. thank you!
dumbcow
  • dumbcow
you could simplify it by using sum formula for arithmetic series \[S = \frac{n (a_1 + a_n)}{2}\]
Vocaloid
  • 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
Vocaloid
  • Vocaloid
^meant to post that earlier, got sidetracked by another question
zmudz
  • zmudz
thanks

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