$1)$Complete this table rounding each decimal to the nearest integer. This should give you a senseof the comparative growth rates of the functions. Note that lg$($n$)$ means python$$s log$2($n$).$ lg$($nn$)$nn nn nnnnnn$($nn$)$ nn$2$ nn$32$nn nn$!12345678910$ For #$2,3,$ and $4,$ solve each summation in two ways: write out all terms of the sum and perform the arithmetic; then use one of the formulas in the class notes to confirm your answer. $2)15$ ii$2$ ii$=13)102$ii ii$=04)$ Follow the same instructions for #$2$ and #$3$; round off this answer to three decimal places. $2$ii$8$ii$=1$ For #$5,$ solve this summation in two ways: write out all terms of the sum, but there will be no arithmetic to perform; then use one of the formulas in the class notes to express the sum as a polynomial function of n$.5)$ nn$1$ ii ii$=1$Asymptotic analysis for #$6$ and #$7$: Determine the Big$-$Oh class of each algorithm. That is$,$ formally compute the worst$-$case running time as we did on class using a table to produce a function that tracks the work required by all lines of code. Include all steps of the algebraic simplification, but you do not need to provide comments to justify each step. $6)$ Arithmetic mean $=$add them all up$,$ and divide by how many$.$ Let the size of the problem $=$ n $=$ the number of entries in the array. $1$ # Input: an array A of real numbers $2$ # Output: the arithmetic mean of the entries in the array $3$ def arithmeticMean$($A$)$: $4$ sum $=05$ count $=06$ for x in A: $7$ sum $+=$ x $8$ count $+=19$ average $=$ sum$/$count $10$ return average $7)$Sum of entries in an upper triangular nxn array. Let the size of the problem $=$ n $=$ thedimension of the nxn matrix. $1234$ # Input: an upper triangular square matrices A where all entries below the diagonal $=0,$ # and an integer n giving the dimension of this nxn matrix # Output: a real number giving the sum of the entries def UpperTriangularMatrixSum $($A$,$ n$)$: $5$ sum $=06$ for i in range$(0,$ n$)$: $7$ for j in range$($i$,$ n$)$: $8$ sum $+=$ A$[$i$][$j$]9$ return sum