isi-entrance 2012 Q17

isi-entrance · India · solved Sequences and series, recurrence and convergence Convergence proof and limit determination

Let $a_1 = 24^{1/3}$ and $a_{n+1} = (a_n + 24)^{1/3}$. Find the integer part of $a_{100}$.

By induction, $a_n < 3$ for all $n$. Hence the integer part of $a_{100}$ is $2$. (A)

Let $a_1 = 24^{1/3}$ and $a_{n+1} = (a_n + 24)^{1/3}$. Find the integer part of $a_{100}$.