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I've been looking at examples and I can't seem to see what they are doing.

For example, the book has:

Suppose that d1, d2, d3 ... is a sequence defined as follows:

d1 = 9/10, d2 = 10/11.

dk = dk-1 * dk-2 for all inegers k >= 3.

Prove that dn =< 1 for all integers n >= 0.

The book says:

Proof (by strong mathematical induction): let the property P(n) be the inequality dn =< 1.

Show that the proeprty is true for n = 1, and n =2:

I understand why they are starting at n = 1, but why are they testing 2 cases? If i had say, d1 = 9/10, d2 = 10/11, d3 = 10/12, then would i have to test for n = 1, n = 2, and n = 3?

They then go onto say,

Show that for any integer k > 2, if the property is true for all integeers i with 1 =< i < k, then it is true for k:

I'm confused on how they are getting k > 2, also how did they figure out that range from 1 = < i < k ?

My problem looks very similar to this one, but it has 3 subscripts instead of one:

http://suprfile.com/src/1/3itfbah/3.jpg [Broken]

I would think k >= 3, becuase thats the problem states, that

ek = ek -1, ek-2, ek-3 for all integersk >= 3

THanks!

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# Strong mathematical induction, how do u figure out the range of the variable?

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