Approximation of $\frac{{}^2}{6}$

$($a$)$ Compute $($using long division$)$ the first $6$ terms in the sequence

$\{S{\}}_k=1^{},S_k=\frac{1}{k^2}$

$($b$)$ It has been proven $($on $1735,$ by Leonhard Euler$)$ that

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{k^2}=\frac{{}^2}{6}$

Find an approximation of $\frac{{}^2}{6}$ using the terms computed in $($a$)$ approximation of $2$

$6$

$1$

$($a$)$ Compute $($using long division$)$ the first $6$ terms in the sequence

$\{\}\backslash$infty

$=1,=1$

$2$

$($b$)$ It has been proven $($on $1735,$ by Leonhard Euler$)$ that

$\backslash$infty $$

$=1$

$1$

$2=2$

$6$