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Let {an}n>= 1

  • Thread starter snaidu228
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  • #1
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Homework Statement


If x is a real number, we de fine [x] as being the largest integer <= x. For example, [1.2] = 1,
[-1.1] = -2, [1] = 1, [11/3]3 = 3, . . .
Let {an}n>=1 be the numerical sequence de fined by:
a1 = 3; and an = a[n/2], for n>=2

(a) Give the terms a1; a2; ... ; a8 of this sequence.
(b) Prove that an = 3; For all n>=  1


Homework Equations





The Attempt at a Solution



I'm not sure what induction has to do with this... I don't really get it.
 

Answers and Replies

  • #2
33,179
4,859


Homework Statement


If x is a real number, we de fine [x] as being the largest integer <= x. For example, [1.2] = 1,
[-1.1] = -2, [1] = 1, [11/3]3 = 3, . . .
Let {an}n>=1 be the numerical sequence de fined by:
a1 = 3; and an = a[n/2], for n>=2

(a) Give the terms a1; a2; ... ; a8 of this sequence.
(b) Prove that an = 3; For all n>=  1


Homework Equations





The Attempt at a Solution



I'm not sure what induction has to do with this... I don't really get it.
Write out a few terms of the sequence to get a feel for what it's doing.
a1 = 3, a2 = ?, a3 = ?, a4 = ? And so on, through a8. That's part a.
 

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