$\%$ Problem $9\mathrm{.}16$

$\%$ The value of can be approximated with the Gregory$-$Leibniz series summation

$\%$ pi$/4=1-1/3+1/5-1/7+1/9-1/11...$

$\%$ or

$\%$ pi $=4-4/3+4/5-4/7+4/9-4/11...$

$\%$ The series converges very slowly. Calculate pi$,$ using a midpoint break loop implemented with a for loop.

$\%$ Determine convergence by comparing successive values of the summation as you add additional terms

$\%$ until the absolute value of the difference between successive sums is less than a convergence criteria, e$,$ of $0\mathrm{.}001.$

$\%$ Set the maximum number of iterations to $3000.$ Hint: Calculate successive terms in the series before you add them to the running total.

$\%$ Since the new term is the difference between the successive sums you can use this value to compare to the convergence criteria.

$\%$ Using this strategy it is not necessary to store both the current and former values of the successive sums.

$\%$ Name your approximate value of pi$,$ my$\_$pi$.$

$\%$ Follow these steps:

$\%1.$ Initialize 'total' to $0$ for summing the series.

$\%2.$ Set the convergence criteria $\text{'}$e$\text{'}$ to $0\mathrm{.}001.$

$\%3.$ Use a for loop with a maximum of $3000$ iterations to calculate the series.

$\%4.$ Within the loop, compute each term and add it to 'total'.

$\%5.$ Implement a midpoint break when the term's absolute value is less than $\text{'}$e$\text{'}.$

$\%6.$ After the loop, assign the computed value to $\text{'}$my$\_$pi$\text{'}.$

$\%$ Use'k' as the counter in the for loop.