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anonymous

  • 5 years ago

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

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  1. amistre64
    • 5 years ago
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    can we induce it?

  2. anonymous
    • 5 years ago
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    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

  3. amistre64
    • 5 years ago
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    2n + 3 ------- n + 3 -3 | 2 3 0 -6 ----- 2 -3 (3) 2 - ----- n+3

  4. amistre64
    • 5 years ago
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    3/n+3 >2 3/2 > n+3 1.5 - 3 > n -1.5 > n

  5. amistre64
    • 5 years ago
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    since a sequence starts at 1 and moves up; then n< -1.5 is not possible is it?

  6. anonymous
    • 5 years ago
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    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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