TASK$-15($MATLAB loops$)$

Consider the sum $\text{'}S\text{'},$ defined in the Figure. It is a function of two parameters, $NO$ and $N.$ Calculate the sum $\text{'}S"$ for $NO=289$ and $N=19388.$

Figure$-15$: Definition of the sum $"S",$ being a function of $N0$ and $N$ and explicit examples of the sum for particular values of input parameters.

$S(N_0,N)=\frac{1}{\sqrt[\phantom{2}]{N_0}+\sqrt[\phantom{2}]{N_0+1}}+\frac{1}{\sqrt[\phantom{2}]{N_0+1}+\sqrt[\phantom{2}]{N_0+2}}+\frac{1}{\sqrt[\phantom{2}]{N_0+2}+\sqrt[\phantom{2}]{N_0+3}}+$dots

$+$dots$+\frac{1}{\sqrt[\phantom{2}]{N-2}+\sqrt[\phantom{2}]{N-1}}+\frac{1}{\sqrt[\phantom{2}]{N-1}+\sqrt[\phantom{2}]{N}}$

Examples :

$N_0=1$;$,N=4$;$,S(1,4)=\frac{1}{\sqrt[\phantom{2}]{1}+\sqrt[\phantom{2}]{2}}+\frac{1}{\sqrt[\phantom{2}]{2}+\sqrt[\phantom{2}]{3}}+\frac{1}{\sqrt[\phantom{2}]{3}+\sqrt[\phantom{2}]{4}}$

$N_0=10$;$,N=12$;$,S(10,12)=\frac{1}{\sqrt[\phantom{2}]{10}+\sqrt[\phantom{2}]{11}}+\frac{1}{\sqrt[\phantom{2}]{11}+\sqrt[\phantom{2}]{12}}+\frac{1}{\sqrt[\phantom{2}]{12}+\sqrt[\phantom{2}]{13}}$

PLEASE, READ ADDITIONAL RECOMMENDATIONS AND ENTER YOUR

$5$ points

ANSWER for TASK$-15$ BELOW:

Round your result for $"S"$ up to two figures after the dot and select the choice $($in the multiple choice answer fields below$),$ most closely matching your numerical answer.

$100\mathrm{.}33$