# Math Is Fun Forum

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## #1 2023-02-17 11:01:47

JoshZ
Guest

### Sum of number sequence

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).

## #2 2023-02-19 03:43:15

Bob
Registered: 2010-06-20
Posts: 9,633

### 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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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