Write a program to calculate the two following sums using loops:

$s={\displaystyle \underset{k=1}{\overset{49997}{}}}\frac{1}{k^2+5k+6},t={\displaystyle \underset{k=49997}{\overset{1}{}}}\frac{1}{k^2+5k+6}$

and calculates $r$ using the simple formula:

$r=\frac{1}{3}-\frac{1}{50000}$

Your program should print out $5$ numbers: first print out $s,$ result of the first sum,

with $\%$f; then print $t,$ the result of the second sum, with $\%$f; then print out both

$r-t$ and $r-s$ using one of $\%f,\%$ e or $\%g,$ depending on which you think is most

useful.

Hint: When the computer calculates these, they will probably not be the same.

However, mathematically they should be the same $-$ try partial fractions if you

want to see why.