The sequence {an} is defined by a1 = 1; an+1 = 4 + 2an^1/3 (The sequence a subscript 1 = 1; a subscript (n plus 1) = 4 + 2a (subscrpit n+1) a raised to the

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The sequence {an} is defined by a1 = 1; an+1 = 4 + 2an^1/3 (The sequence a subscript 1 = 1; a subscript (n plus 1) = 4 + 2a (subscrpit n+1) a raised to the

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The sequence {an} is defined by a1 = 1; an+1 = 4 + 2an^1/3 (The sequence a subscript 1 = 1; a subscript (n plus 1) = 4 + 2a (subscrpit n+1) a raised to the power of 1/3)

Use mathematical induction to prove that 1 <_ an <_ 8 for any nEZ+

Can someone please explain how to solve this. I understand the induction method but something somewhere escapes me and i am not able to solve this one.

christosmit84 Oct 9, 2013

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Melody · Answer 1 · 2013-10-09T10:59:44

I am not sure that I understand the question.
Do you mean

a ₁=1
a _n+1 = 4 + 2(a _n) ^1/3

so the sequence is 1, 6, 4+2*(6 ^1/3), 4 + 2[4+2*6 ^1/3] ^1/3, .....

Also, what is nEZ+ I am not familiar with this notation.

It does look hard. If you tell me that my interpretaion is correct then I will give it a go.

Melody · Answer 2 · 2013-10-09T12:06:10

I would still like to know what nEZ+ stands for but this it the solution.

Maths induction 131009.jpg

The sequence {an} is defined by a1 = 1; an+1 = 4 + 2an^1/3 (The sequence a subscript 1 = 1; a subscript (n plus 1) = 4 + 2a (subscrpit n+1) a raised to the

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The sequence {an} is defined by a1 = 1; an+1 = 4 + 2an^1/3 (The sequence a subscript 1 = 1; a subscript (n plus 1) = 4 + 2a (subscrpit n+1) a raised to the

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