$\%$define the range

nn$=20$;

$\%$ define the loop for calculation of error

sum$1=0$;sum$2=0$;

for ii$=1$:nn;

$\%$ formula $1$ and $2$ values

sum$1=0$;sum$2=0$

for jj$=1$:ii

sum$1=$sum$1+(-1)^($jj$-1)*4^($jj$-1)/$factorial$($jj$-1)$;

sum$2=$sum$2+4^($jj$-1)/$factorial$($jj$-1)$;

end

f$\_1\_$val$($ii$)=$sum$1$;

f$\_2\_$val$($ii$)=1/$sum$2$;

$\%$ formula $1$ and $2$ true errors

e$\_$t$\_1($ii$)=$abs$($f$\_1\_$val$($ii$)-$exp$(-4))/$exp$(-4)*100$;

e$\_$t$\_2($ii$)=$abs$($f$\_2\_$val$($ii$)-$exp$(-4))/$exp$(-4)*100$;

end;

$\%$ formula $1$ and $2$ relative approxilate errors

e$\_$a$\_1=[]$;

e$\_$a$\_2=[]$;

e$\_$a$\_1(1)=0$;

e$\_$a$\_2(1)=0$;

for kk$=2$:nn;

e$\_$a$\_1($kk$)=$abs$($f$\_1\_$val$($kk$-1)-$f$\_1\_$val$($kk$))/$exp$(-4)*100$;

e$\_$a$\_2($kk$)=$abs$($f$\_2\_$val$($kk$-1)-$f$\_2\_$val$($kk$))/$exp$(-4)*100$;

end

T$=$table$($f$\_1\_$val',e$\_$t$\_1\text{'},$e$\_$a$\_1\text{'},$f$\_2\_$val',e$\_$t$\_2\text{'},$e$\_$a$\_2\text{'})$;

filename$=\text{'}$C:$\backslash$Users$\backslash$user$\backslash$Documents$\backslash$MATLAB$\backslash$rel$\_$tru$\_$error.xlsx$\text{'}$;

writetable$($T$,$filename,'sheet',$1,$'WriteVariableNames',false$)$;