anonymous
  • anonymous
how to prove that the sequence defined by (2n + 3) / (n + 3) is always less or equal than 2, for every n? ( without taking the sequence limit? Thanks
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
can we induce it?
anonymous
  • anonymous
2n + 3 / n + 3 = 2 Therefore it simplifies to 2n + 3 = 2n + 6 which is noot possible Therefore n cannot be 2 If 2n + 3 / n + 3 = 3 ( >2) 2n + 3 = 3n + 9 n = -6 If 2n + 3 / n + 3 = 1 ( <2) 2n + 3 = n + 3 n = 0 So i think it is all possible except n = 2
amistre64
  • amistre64
2n + 3 ------- n + 3 -3 | 2 3 0 -6 ----- 2 -3 (3) 2 - ----- n+3

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amistre64
  • amistre64
3/n+3 >2 3/2 > n+3 1.5 - 3 > n -1.5 > n
amistre64
  • amistre64
since a sequence starts at 1 and moves up; then n< -1.5 is not possible is it?
anonymous
  • anonymous
Hmm...induction; (2n+3)/n+3 <=2 Proving this for the first natural number; 5/4<=2 [yes] Lets prove this is true 2(n+1)+3 / n+1+3 <=2 2n+5 <= 2n + 8 5<=8 [true] Done!

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