A

9. Let {a_n} be a sequence such that a₀ = 1 and

(n² +2)a_n+1 – (n² + 1)pa_n = 0 for n >= 0.

What are all the values of p for which the series

is absolutely convergent?

A. {p \| p > 1}	B. {p \| p < -1}	C. {p \| \|p\| < 1}
D. {p \| \|p\| < 2}	E. {p \| \|p\| < 1/2}

Solution: The answer is C

Since,

By the ratio test, if

Then,

is absolutely convergent for |p| < 1. Since,

Then,

is absolutely convergent for all values of p such that –1 < p < 1.

A. {p \| p > 1}	B. {p \| p < -1}	C. {p \| \|p\| < 1}
D. {p \| \|p\| < 2}	E. {p \| \|p\| < 1/2}