MathDB

Let

a_1,a_2,a_3,\ldots,a_{250}

be real numbers such that

a_1=2

and

a_{n+1}=a_n+\frac{1}{a_n^2}

for every

n=1,2, \ldots, 249

. Let

x

be the greatest integer which is less than

\frac{1}{a_1}+\frac{1}{a_2}+\ldots+\frac{1}{a_{250}}

How many digits does

x

have?
Proposed by Miroslav Marinov, Bulgaria

A7