doubt how kn - k is coming plz explain what is the purpose

Question

iam confused

Comments

Then put k = n-1

to get T(1) for termination.

So you will get 

T(n) = (n-1)*n + T(1) => n² - n + 1 => O(n²)

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@Ashwin Kulkarni thanks bro but  iam asking why everytime we take   till  T(N-1) AND T(N-2) 

what if i write T(n) = T(n-2) + n + (n-1)   can we solve like this