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I know that the sequences meets the following:

[tex](n+1)(a_{n+1}-a_n)=n(a_{n-1}-a_n)[/tex]

I've got the feeling that this sequence is alternating or decreasing, but I was unable to prove it.

Usually I use induction to prove things about such inductive sequence but in this case I don't have real values t o the first terms of the sequence so I don't have an idea how to even begin inductive prove.

[tex](n+1)(a_{n+1}-a_n)=n(a_{n-1}-a_n)[/tex]

I've got the feeling that this sequence is alternating or decreasing, but I was unable to prove it.

Usually I use induction to prove things about such inductive sequence but in this case I don't have real values t o the first terms of the sequence so I don't have an idea how to even begin inductive prove.

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