The famous number $\pi=3.1415...$ can be found by adding together certain patterns of numbers. There
are many such patterns, and we'll use one of them here. When finding $\pi$ in this manner, the more numbers you add
the better your result for $\pi$ will be. This is called the "infinite series" approach to finding $\pi$.

The infinite series we'll use for $\pi$ is this one $\frac{\pi^2}{6}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...$. As you can see, there is a definite pattern on the right side. Just count from $1$ to $2$ to $3$, etc., always putting the count number (squared) into the denominator of a fraction, with $1$ as the numerator. If you keep adding these fractions, you'll get $\pi^2/6$.

The infinite series we'll use for $\pi$ is this one $\frac{\pi^2}{6}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...$. As you can see, there is a definite pattern on the right side. Just count from $1$ to $2$ to $3$, etc., always putting the count number (squared) into the denominator of a fraction, with $1$ as the numerator. If you keep adding these fractions, you'll get $\pi^2/6$.

`sum`

to add up ten terms of the $\pi$ sum shown above.
Type your code here:

See your results here:

The code will not run as is! Think a bit now. What should the variable

`sum`

be equal to in the `sum=`

line as you start computing $\pi$?
Next, in the body of the `for-loop`

, what should you add to the variable `sum`

with each count through the loop? (Hint: think
of the $\pi$ pattern discussed above.) Lastly, in the `pi=math.sqrt( )`

line, what will you take the square root of
to arrive at $\pi$ from the sum of your fractions? (Hint: from the formula above, it looks like $\pi=\sqrt{6\cdot sum}$.) Can you get this
all fixed and find an approximation for $\pi$?