Math Is Fun Forum

JoshZ

Guest

Sum of number sequence

Could anyone please help me prove the question below:

Question: Assume that we have a number sequence a with a_1=1/2 and the general term a_n=square(a_(n-1)) + a_(n-1) for all n>=2. Prove that the following inequality holds for all k>=1:

1/(a_1 + 1) + 1/(a_2 + 1) + ... + 1/(a_k + 1) < 2.

Note that the notation a_(n-1) denotes the symbol a with the subscript (n-1).

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Sum of number sequence

hi JoshZ

Welcome to the forum.

I don't have a full proof forthis but the following may help.

So maybe you can show that each term < a term in a sequence (GP ?) that sums from below to 2.

Bob

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