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Found problems: 1

2013 Bogdan Stan, 4
Tags: Cesaro-Stolz , real analysis , Seqeunce , Sequence
Let be a sequence $ \left( x_n \right)_{n\ge 1} $ having the property that $$ \lim_{n\to\infty } \left( 14(n+2)x_{n+2} -15(n+1)x_{n+1} +nx_n \right) =13. $$ Show that $ \left( x_n \right)_{n\ge 1} $ is convergent and calculate its limit. [i]Cosmin Nițu[/i]