Cannot understand exercise 1

#1

please explain exercise 1 unable to understand from video

#2

we are required to find time complexity
so

we see
that i runs from [0,n-1] so this loops runs N times

thenwe have j from [i+1 , k]
so in first iteration when i =0 jth loop runs k times
then when i = 1 j loop iterates k-1 times
then k-2 times and so on

so in total jth loop runs
k*k-1 * k-2 … 1
that is sum of k numbers
k * (k+1) /2
that gives time complexity O(k^2)
and then O ( N ) times is the outer loop
so total would be O ( N+ k^2)

it would had be O ( N * K )
had the inner loop been j = 0 ; j <= k ; j++
but since here the loop is
j= i+1 ; j <= k ; j++

so no of inner iteration reduce with increasing i hence
we have this time complexity

#3

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