Given the following Pseudocode for a recursive algorithm designed to calculate the sum of squares from $1$ to n$.$

function sumOfSquares$($n$)$

if n $==1$

return $1$

else

return n$*$n $+$ sumOfSquares$($n$-1)$

a$)$ Perform a line$-$by$-$line analysis to derive the precise running time T$($n$)$ of the given recursive algorithm. $(4$ pts$)$

b$)$ Convert the recurrence relation T$($n$)$ into a closed form using the iteration method. $(3$ pts$)$

c$)$ Determine the time complexity of the algorithm using Big$-$O notation. $(1$ pts$)$

d$)$ Compare the recursive version with the iterative version of the same problem in terms of time complexity and space complexity. $(2$ pts$)$