Sum $=4{\displaystyle \underset{?}{\overset{?}{}}}(-1)i$

$2i+1$ write a serial program in $C$ to calculate sum of given expression using point to point communication

$9$:$08$PM $\frac{?}{?}$

In this assignment, you will write both serial and parallel programs to calculate the Sum using the following formula:

Sum $=4{\displaystyle \underset{i=0}{\overset{n}{}}}\frac{(-1{)}^i}{2i+1}$

You will write a serial C program $($Sum$\_$Serial.c$)$ to calculate the sum Sum and validate the correctness of your serial implementation. You will modify the serial program into two parallel programs, namely Sum$\_$MPI$\_$v$1.$c and Sum$\_$MPI$\_$v$2.$c$.$ In Sum$\_$MPI$\_$v$1.$c$,$ utilize only MPI pointto$-$point communication functions $($MPI$\_$Send and MPI$\_-\frac{?}{\text{b}\text{a}\text{r}}(-)$ ecv$)$ for message passing. In Sum$\_$MPI$\_2.$c$,$ implement your parallel solution using collective communication functions. Compile and execute these programs on magnolia HPC cluster to obtain the results. The user can specify $n$ when executing your programs.

Present your results in the following two tables. Table $1$ should include a comparison of the Sum results obtained by three programs with respect to different $n$ numbers. For the two parallel programs, you can set $p=1$ and $p=8$ where $p$ is the number of processes. Ensure that the Sum results exhibit six digits to the right of the decimal point.

Table $1$: Comparison of Sum results with respect to different $n$ and $p$ values.

$\backslash$table$[[$Sum$,$Sum$\_$Serial.c$,$Sum MPI v$1.$c$,$Sum MPI v$2.$c$],[p=1,p=8,p=1,p=8$