Question

Let $S = sum_{n=1}^{infty} a_n$ be an infinite series such that the $k^{th}$ partial sum is $S_k = 8 - frac{4}{k^2}$. (a) What are the values of $sum_{n=1}^{10} a_n$ and $sum_{n=4}^{16} a_n$? $sum_{n=1}^{10} a_n = $ $sum_{n=4}^{16} a_n = $ (b) What is the value of $a_3$? $a_3 = $ (c) Find a general formula for $a_n$ for $1 < n$. $a_n = $ (d) Find the sum $sum_{n=1}^{infty} a_n$. $sum_{n=1}^{infty} a_n = $

          Let $S = sum_{n=1}^{infty} a_n$ be an infinite series such that the $k^{th}$ partial sum is $S_k = 8 - frac{4}{k^2}$.

(a) What are the values of $sum_{n=1}^{10} a_n$ and $sum_{n=4}^{16} a_n$?
$sum_{n=1}^{10} a_n = $
$sum_{n=4}^{16} a_n = $

(b) What is the value of $a_3$?
$a_3 = $

(c) Find a general formula for $a_n$ for $1 < n$.
$a_n = $

(d) Find the sum $sum_{n=1}^{infty} a_n$.
$sum_{n=1}^{infty} a_n = $

$Let S = sumn=1^infty an be an infinite series such that the k^th partial sum is Sk = 8 - frac4k^2. (a) What are the values of sumn=1^10 an and sumn=4^16 an? sumn=1^10 an = sumn=4^16 an = (b) What is the value of a3? a3 = (c) Find a general formula for an for 1 < n. an = (d) Find the sum sumn=1^infty an. sumn=1^infty an =$

Added by Felipe S.

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