Home > Analysis > IMC 2012 Problem 7

IMC 2012 Problem 7


Define the sequence {a_0,a_1,..} inductively by {a_0=1, a_1=1/2} and

\displaystyle a_{n+1}=\frac{na_n^2}{1+(n+1)a_n} \text{ for }n \geq 1.

Show that the series {\displaystyle \sum_{k=0}^\infty \frac{a_{k+1}}{a_k}} converges and determine its value.

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