Write a C$++$ Program with functions that will calculate the value of the Nilakantha

Somayaji's Series:

$3+{\displaystyle \underset{k=1}{\overset{n}{}}}(\frac{-1^{k}4}{2k(2k+1)(2k+2)})$

The user will enter any positive number, the program will calculate the value of the

series using a recursive function, and then, calculate the error percentage of the

terms in relation to $$ in another function. The number $N$ should be a positive

integer lower than $200.$ Format your results to $10$ decimal places $($ex:

$0\mathrm{.}0000000000\%.$

The error percentage formula is:

Error Percentage $=\frac{|\text{E}\text{x}\text{p}\text{e}\text{r}\text{i}\text{m}\text{e}\text{n}\text{t}\text{a}\text{l}\text{V}\text{a}\text{l}\text{u}\text{e}-\text{T}\text{h}\text{e}\text{o}\text{r}\text{e}\text{t}\text{i}\text{c}\text{a}\text{l}\text{V}\text{a}\text{l}\text{u}\text{e}|}{\text{T}\text{h}\text{e}\text{o}\text{r}\text{e}\text{t}\text{i}\text{c}\text{a}\text{l}\text{V}\text{a}\text{l}\text{u}\text{e}}100\%,$

where the Experimental Value is the value of the quotient, as calculated from the

numbers of the series, and the Theoretical Value is $.$ Use the C$++$ Math constants

in the cmath preprocessor.