It is known that:

$cos(x)={\displaystyle \underset{k=0}{\overset{}{}}}\frac{(-1{)}^k{x}^{2k}}{(2k)!}$

Truncate the series to compute the first $8$ estimates $($i$.$e$.k=0,1,$cdots,$7)$ for $x=\frac{}{5}.$ You must use a for loop. All calculations and printing the table described below should be done from within the loop. Arrange your results in a table using fprintf that has column $1$ as the $\text{'}$# of Terms' included in the estimate $($not the k value$),$ the second column the 'Estimate', the third column the 'True Error' and the fourth column the 'Magnitude of the Approximate Percent Relative Error', 'MAPRE'. Express everything, except the number of terms, in decimal format with $10$ digits after the decimal point. The header should look exactly like this:

# of terms Estimate True Error

MAPRE