Consider the series ${\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{k^2}.$

$($a$)$ In $1-2$ sentences, explain why this series is NOT geometric.

$($b$)$ Use one of the series tests to confirm that this series converges.

$($O$)$ Find the first five terms in the sequence of partial sums. Then, based on those terms, make a guess for what the series converges to$.$

$($d$)$ Perform an internet search to determine what this series actually converges to$.$ Respond to the following prompts:

What is the name of the mathematician who found the value of the series?

In what century did that mathematician discover the value?

Write $5-6$ sentences about how the mathematician found the value.